Answer:
The probability is 0.503
Step-by-step explanation:
If the ghost appearances occur in the house according to a Poisson process with mean m, the time between appearances follows a exponential distribution with mean 1/m. so, the probability that the next ghost appearance happens before x hours is equal to:
[tex]P(X\leq x)=1-e^{-xm}[/tex]
Then, replacing m by 1.4 ghosts per hour we get:
[tex]P(X\leq x)=1-e^{-1.4x}[/tex]
Additionally, The exponential distribution have a memoryless property, so if it is now 1:00 p.m. and we want the probability that ghost appear before 1:30 p.m., we need to find the difference in hours from 1:00 p.m and 1:30 p.m. no matter that the last ghost appearance was at 12:35 p.m.
Therefore, there are 0.5 hours between 1:00 p.m. and 1:30 p.m, so the probability that the 7th ghost will appear before 1:30 p.m is calculated as:
[tex]P(x\leq 0.5)=1-e^{-1.4*0.5} =0.503[/tex]
Final answer:
The probability that the 7th ghost will appear before 1:30 p.m. in an old house in Pomona, CA can be calculated as approximately 0.5034, or 50.34%. This calculation is based on the Poisson distribution, with a rate of 1.4 ghosts per hour and the last ghost appearance occurring at 12:35 p.m.
Explanation:
The probability of the 7th ghost appearing before 1:30 p.m. can be calculated using the Poisson distribution. We know that the rate of ghost appearances is 1.4 ghosts per hour, which means the average time between ghost appearances is 1/1.4 hours. From 12:35 p.m. to 1:00 p.m., there are 25 minutes, or 25/60 hours. So, the probability that the 7th ghost will appear before 1:30 p.m. is equal to the probability that there will be at least 1 ghost in the remaining time, i.e., the probability that at least one ghost appears in the next 30 minutes.
We can use the complementary probability method to calculate this. The complementary probability is the probability that none of the ghosts appears in the next 30 minutes. Since the time follows a Poisson process, we can use the Poisson probability formula. Let's calculate:
Calculate the average rate of ghost appearances in the next 30 minutes:Rate = (1.4 ghosts/hour) * (30/60 hours) = 0.7 ghostsCalculate the probability of no ghost appearing:P(X = 0) = (e^(-0.7) * 0.7^0) / 0! = e^(-0.7) ≈ 0.4966Calculate the complementary probability:P(at least 1 ghost) = 1 - P(no ghost) = 1 - 0.4966 ≈ 0.5034Therefore, the probability that the 7th ghost will appear before 1:30 p.m. is approximately 0.5034, or 50.34%.
Simplify: 1/4(-12+4/3)
Zoe made 6 3/4 cups of fruit salad for a picnic at the picnic they ate 1/3 of the fruit salad how much fruit salad did they eat
6 3/4 = 27/4
27/4 * 1/3 = 27/12
27/12 = 9/4
Answer: 9/4 cups
To find out how much fruit salad was eaten, convert the mixed number to an improper fraction and multiply by the fraction representing the amount eaten.
Explanation:To calculate how much fruit salad was eaten, we need to find 1/3 of 6 3/4 cups. First, we convert the mixed number 6 3/4 to an improper fraction by multiplying the whole part (6) by the denominator (4) and adding the numerator (3) to it. This gives us 27/4 cups. Next, we multiply 27/4 by 1/3, which can be simplified to 9/4. So, they ate 9/4 cups of fruit salad.
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Refer to speeds at which cars pass through a checkpoint on the highway. Assume the speeds are normally distributed with a population mean of 61 miles per hour and a population standard deviation of 4 miles per hour. Calculate the probability that the next car passing will be travelling more than 66 miles per hour.
Answer:
Probability that the next car passing will be travelling more than 66 miles per hour is 0.10565.
Step-by-step explanation:
We are given that the the speeds are normally distributed with a population mean of 61 miles per hour and a population standard deviation of 4 miles per hour.
Let X = speed of car
The z-score probability distribution for normal distribution is given by;
Z = [tex]\frac{ X-\mu}{\sigma}} }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean speed = 61 miles per hour
[tex]\sigma[/tex] = standard deviation = 4 miles per hour
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, Probability that the next car passing will be travelling more than 66 miles per hour is given by = P(X > 66 miles per hour)
P(X > 66) = P( [tex]\frac{ X-\mu}{\sigma}} }[/tex] > [tex]\frac{ 66-61}{4}} }[/tex] ) = P(Z > 1.25) = 1 - P(Z [tex]\leq[/tex] 1.25)
= 1 - 0.89435 = 0.10565
So, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.25 in the z table which has an area of 0.89435.
Hence, the probability that the next car passing will be travelling more than 66 miles per hour is 0.10565.
Final answer:
The probability that the next car passing will be traveling more than 66 miles per hour, given a mean speed of 61 mph and standard deviation of 4 mph, is approximately 10.56%.
Explanation:
To calculate the probability that the next car passing will be traveling more than 66 miles per hour, given the speeds are normally distributed with a mean of 61 miles per hour and a standard deviation of 4 miles per hour, we use the Z-score formula.
The Z-score formula is: Z = (X - μ) / σ, where μ is the mean, σ is the standard deviation, and X is the value we're interested in.
Substitute the given values into the formula to find the Z-score for 66 miles per hour.
Z = (66 - 61) / 4 = 5 / 4 = 1.25.
Next, we look up the Z-score of 1.25 on the standard normal distribution table or use a calculator to find the area to the left of Z. The area to the left of Z=1.25 is approximately 0.8944. To find the probability of a car traveling more than 66 miles per hour, we subtract this value from 1.
Probability = 1 - 0.8944 = 0.1056.
Therefore, the probability that the next car passing will be traveling more than 66 miles per hour is approximately 10.56%.
Al find a new supplier. He can buy raw peanuts for $.30 for a pound. If he sells the peanuts in a .2-pound bags for $2.50 a bag, How much profit is made on each bag
Answer:
$1.9
Step-by-step explanation:
2 pound bag (when he bought) =.30×2=$0.6
when he sells, price is $2.50.
Profit for each bag= $2.5-$0.6=$1.9
A simple random sample of 5 months of sales data provided the following information: Month:12345 Units Sold:9480859492 (a)Develop a point estimate of the population mean number of units sold per month. x
Answer:
89 units
Step-by-step explanation:
-The population's mean point estimate is equivalent to the sample mean.
Given the 5 month units sold is 94,80,85,94 and 92
-Mean is the average of the units sold over the 5 month period:
[tex]\bar X=\frac{\sum {x_i}}{n}\\\\=\frac{94+80+85+84+92}{5}\\\\=89[/tex]
Hence, the point estimate for the population mean is 89 units
A manager recorded how many hours each of 11 cashiers worked in a week. Which interval contains the median number of hours worked?
Answer:
Step-by-step explanation:
Hello!
In descriptive statistics, the median is a measurement of center position. It separates the sample in halves. (bottom 50% from upper 50%)
The manager took a sample of 11 cashiers and recorded the worked hours in a week
To identify the median you have to calculate it's position:
The position is calculated as
PosMe= (n+1)/2= (11+1)/2= 6 cashier
This means that the Median of hours worked is a week observed corresponds to the 6th cashier (after ordering the data from lowest to highest)
If you observe the histogram, the x-axis corresponds to worked hours and the y-axis shows the number of workers.
The workers were already arranged from least hours worked to most hours worked.
The first interval corresponds to 0-10 worked hours and two workers recorded these working times.
The second interval corresponds to 10-20 worked hours and three workers recorded these working times.
In the third interval of 20-30 hours, no workers recorded these working times.
The fourth interval corresponds to 30 - 40 worked hours and 5 workers recorded these working times.
The fifth interval corresponds to 40 - 50 worked hours and only one worker recorded these working hours.
The first five workers were recorded in the first two intervals and the sixth worker was recorded in the fourth interval. So the interval that contains the median number of hours worked is "30 - 40 hours"
I hope this helps!
The interval that contains the median number of hours worked is "30 - 40 hours"
The manager took a sample of 11 cashiers and recorded the worked hours in a week
To identify the median you have to calculate it's position:
The position is calculated as
PosMe= (n+1)/2= (11+1)/2= 6 cashier
The fourth interval corresponds to 30 - 40 worked hours and 5 workers recorded these working times.
The first five workers were recorded in the first two intervals and the sixth worker was recorded in the fourth interval. So the interval that contains the median number of hours worked is "30 - 40 hours"
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Which equation has the components of 0 = x2 - 9x - 20 inserted into the quadratic formula correctly?
O
x
= -9 V(-9)2 - 4(1)(-20)
x= 91V(- 9)2 - 4(1)(20)
2(1)
x= 9:(-92 - 4(1)(-20).
2(1)
x= -9 1(-9)2 + 4(1)(-20)
2(1)
Answer:
c
Step-by-step explanation:
just did it on the assignment
FIND THE AREA OF THE SHADED REGION
Answer: 40in²
Step-by-step explanation:
To find the area of the shade region, considering the diagram, the diagonal of the rectangle has divided the figure into two equal half. So, one is shaded and the other not shaded. So the shaded region is a right angled triangle,. So the formula for finding the area of a triangle need to be applied.
Area. = 1/2 × b × h
= 1/2 × 10 × 8
= 40in²
Find the volume of a sphere with a diameter of 20 inches
Answer:
V≈4188.79in³
Step-by-step explanation:
4.188.79in3
HELP! will give brainliest if given right answers
7. tails, odd, 4
P(tails) = 1/2
P(odd) = 3/6 = 1/2
P(4) = 1/6
P(tails then odd then 4) = (1/2)×(1/2)×(1/6) = 1/24 ≈ 0.041666
Answer: 1/24, 4.2%
8. tails, 6 or 1, 3
P(6 or 1) = 2/6 = 1/3
P(3) = 1/6
P( tails, 6 or 1, 3) = (1/2)(1/3)(1/6) = 1/36 ≈ 0.027777
Answer: 1/36, 2.8%
9. heads, not 2, even
P(heads) = 1/2
P(not 2) = 5/6
P(even) = 1/2
P(heads, not 2, even) = (1/2)(5/6)(1/2) = 5/24 ≈ 0.208333
Answer: 5/24, 20.8%
Answer:
7. 1/24 = 4.2%
8. 1/36 = 2.8%
9. 1/6 = 16.67%
All percentages are rounded
(06.01)
A class has 21 girls and 12 boys. What is the probability that a boy's name is drawn at random? (5 points)
Answer:
In my opinion I think the answer is C.12/33
Step-by-step explanation:
this would be the answer because...
1. First, add up the amount of boys and girls
21 girls+ 12 boys= 33 total
2. Next, since its asking for the probability for a boys name to de drawn at random, your going to divide 12 by 33
12/33Answer:
it is c i took test good luck
Step-by-step explanation:
sike i lied your a is mine lol
Match the number to the value of its 7
Answer:
The first one is matched with 700,000
The second one is matched with 7
The third one is matched with 70
The fourth one is matched with 70,000
Step-by-step explanation:
Look at where the 7 is in the number, and replace all the digits to the right of it with 0's. Get rid of the digits to the left of the 7, if any
Answer:
1-->1
2-->3
3-->2
4-->4
Step-by-step explanation:
In the first number the 7 is in the the hundred thousands place. In the second the 7 is in the ones place. In the third the 7 is in the tens place. In the fourth the 7 is in the ten thousands place.
A carousel has eight evenly spaced seats shaped like animals. During each ride, the carousel makes between 8 and 9 clockwise revolutions. At the end of one ride, the carousel stops so that the lion is in the position where the zebra was when the ride started. Through how many degrees did the carousel rotate on this ride
Answer:
2931 + 51.4n/7 degrees where n is the number of animal from the lion to the zebra in the clockwise direction.
Step-by-step explanation:
We don't have details on the positions of the lion and the zebra prior to revolution but suppose the zebra is n animal away from the lion where n could be in the range of 0 to 6 in the clockwise direction. If n = 0, the zebra is next to the lion in line, and if n = 6, the zebra is right behind the lion.
In angular term, since all 8 animals are evenly spaced, there are 7 space in between them, each of them would span an angle of 360/7 degrees
Then the angular distance between the zebra and the lion is (n+1)360/7 degrees
If the carousel makes between 8 and 9 revolutions then the total angular distance is 8*360 + (n+1)360/7 = 2931 + 51.4n/7 degrees
Answer:
-2970, -3320
Step-by-step explanation:
The carousel makes between 8 and 9 clockwise revolutions
the position of the lion rotated to that of the zebra is two steps
now,
1 revolution = 360 degrees accomplished in 8 steps
1 step = 360/8 = 45 deg
=> position of lion rotated to zebra = 2 × 45 = 90 deg
if 1 revolution = 360 accomplished in 9 steps
then
1 step = 360/9 = 40 deg
=> position of lion rotated to zebra = 2 × 40 = 80 deg
since the rotation is in clockwise direction, a negative sign is required
FOR 8 Revolutions
in total the carousel rotates
-[8(360) + 90] degrees
= -2970 degrees
FOR 9 revolution
in total the carousel rotates
-[9(360) + 80] degrees
= -3320 degrees
Which points on the graph represent values that could be in the table? A B C D
Answer:
uhhh
Step-by-step explanation:
uh I don't see the graph
Answer:
D and B
Step-by-step explanation:
Which would you use to solve the equation? Check all that apply.
12.7 = j – 3.4
Subtract 3.4 from both sides of the equation.
Add 3.4 to both sides of the equation.
12.7 + 3.4 = 16.1, so j = 16.1.
12.7 – 3.4 = 9.3, so j = 9.3.
Substitute 9.3 for j to check the solution.
Substitute 16.1 for j to check the solution.
Answer:
the answer is B,C,F
Step-by-step explanation:
The correct options are,
1. Add 3.4 to both sides of the equation.
2. 12.7 + 3.4 = 16.1, so j = 16.1.
3. Substitute 16.1 for j to check the solution.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
The steps to solve the equation: 12.7 = j - 3.4 are as follows,
Add 3.4 to both sides of the equation,
12.7 + 3.4 = j
Solve for j,
16.1 = j
So the solution is j = 16.1
To check the solution, you would substitute 16.1 for j in the original equation and see if both sides are equal.
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BeanPod Groceries will deliver. The delivery fee is $9.95 for a minimum order of $60, which drops to $6.95 for orders of $100 or more. Your order comes to $99.48. If you add a last-minute item costing $1.99 what will your final bill be?
Answer:
$99.44 + $1.99 = $101.47
Delivery fee: $6.95
Final bill: $101.47 + 6.95 = $108.42
The final bill will be either $109.43 or $108.42, depending on whether the last-minute item is included in the order.
Explanation:To calculate the final bill, we need to consider two scenarios: the order without the last-minute item and the order with the last-minute item. First, let's calculate the delivery fee for an order without the last-minute item. Since the order total is $99.48, which is less than $100, the delivery fee will be $9.95. Now, let's calculate the final bill by adding the delivery fee to the order total: $99.48 + $9.95 = $109.43.
Next, let's calculate the delivery fee for an order with the last-minute item. Since the order total will be $101.47 ($99.48 + $1.99), which is more than $100, the delivery fee will be $6.95. To calculate the final bill, we need to add the delivery fee to the updated order total: $101.47 + $6.95 = $108.42.
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Make x the subject of m =n+x/p
Answer:
[tex]x = p( m - n)[/tex]
Step-by-step explanation:
[tex]m = n + \frac{x}{p} \\ m - n = \frac{x}{p} \\ p(m - n) = \frac{x}{p} \times p \\ \\ x = p(m - n)[/tex]
Determine the slope of the line which contains the following points.
(-3,5) and (2,-6)
Answer:
I like it when im high marks a lil by and he say he fly but he dono ha ta fly OoOoooOoOoOOoO
Step-by-step explanation:
According to a study conducted by an organization, the proportion of Americans who were afraid to fly in 2006 was 0.10. A random sample of 1 comma 100 Americans results in 121 indicating that they are afraid to fly. Explain why this is not necessarily evidence that the proportion of Americans who are afraid to fly has increased.
Answer:
Event is not unusual(p>0.05).
Step-by-step explanation:
Given that :
[tex]p=0.10\\\\n=1100\\\\x=121[/tex]
#The sample proportion is calculated as:
[tex]\hat p=\frac{x}{n}\\\\=\frac{121}{1100}\\\\=0.1100[/tex]
#Mathematically, the z-value is the value decreased by the mean then divided the standard deviation :
[tex]z=\frac{\hat p- p}{\sqrt{\frac{p(1-p)}{n}}}\\\\\\\\=\frac{0.11-0.10}{\sqrt{\frac{0.10(1-0.10)}{1100}}}\\\\\\=1.1055[/tex]
#We use the normal probability table to determine the corresponding probability;
[tex]P(X\geq 121)=P(Z>1.1055)\\\\=0.1314[/tex]
Hence, the probaility is more than 0.05, thus the event not unusual and thus this is not necessarily evidence that the proportion of Americans who are afraid to fly has increased.
George works for a shipping company, loading packages into a truck. How much work does George do on a 2-kg package when he lifts it to a height of 1.8 m?
Answer:
Work done by george = 35.28J
Step-by-step explanation:
We are given;
Mass; m = 2 kg
Height;h = 1.8 m
Now, we want to find how much work does George do on a 2-kg package at the height of 1.8m.
This is a potential energy problem.
The formula for work done is therefore;
W = mgh
Where;
m is mass
g is acceleration due to gravity which has a constant value of 9.8 m/s²
h is height
Thus, plugging in relevant values;
W = 2 x 9.8 x 1.8
W = 35.28 J
Final answer:
The work done by George on the 2-kg package when he lifts it to a height of 1.8 meters is calculated using the equation W = mgh, which results in 35.28 joules.
Explanation:
The question How much work does George do on a 2-kg package when he lifts it to a height of 1.8 m? requires the calculation of the work done against the force of gravity. To find the work done, the equation W = mgh is used, where W is the work done in joules, m is the mass in kilograms, g is the acceleration due to gravity (9.8 m/s2), and h is the height in meters.
To solve for the work done in this case: W = (2 kg)(9.8 m/s2)(1.8 m).
When you calculate this, it gives you the work done by George as W = 35.28 J (joules).
find an equation equivalent to r= 1+2 = sin theta in rectangular coordinates
Answer:
C
Step-by-step explanation:
[tex]x^{2}[/tex]+[tex]y^{2}[/tex]= [tex]\sqrt{x^{2}+y^{2} }[/tex]+2y
Answer:
The equation of equivalent is,[tex]x^{4}+ y^{4} +3 y^{2} +2x^{2} y^{2} -4y^{3} -4 x^{2} y-x^{2} =0[/tex]
Step-by-step explanation:
Definition of equivalent equation:If two systems of equations have the same solution, they are equivalent (s). This article explains how to determine whether two systems are equal. Equivalent systems are sets of equations that have the same solution.
Given, r = 1+2sinФ
[tex]r^{2} =r+2rsin[/tex]θ
[tex]x^{2}+ y^{2} =r+2y\\x^{2} + y^{2} -2y=r\\[/tex]
Squaring, both side:
[tex](x^{4} +y^{4} -2 y^{2}) = r^{2} \\x^{4}+ y^{4} + 4y^{2}+2 x^{2} y^{2} - 4y^{3} -4x^{2} y =x^{2} +y^{2} \\x^{4} + y^{4} +3 y^{2} +2 x^{2} y^{2} -4y^{3} -4x^{2} y^}-x^{2} =0[/tex]
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A mechanic finds that 30% of his customers own foreign cars, and that 40% own dogs. Assuming that these events are independent, what percent of the customers have neither a foreign car nor a dog
Answer:
42%
Step-by-step explanation:
Answer:
Since the events are independent, 30% of his customers have neither a foreign car nor a dog.
Step-by-step explanation:
Let the total number of his customers = 100.
Since the events are independent,
customers with foreign cars + customers that own dogs + customers that have neither a foreign car nor a dog = 100.
But,
Customers with foreign cars = 30% = 30
Customers that own dogs = 40% = 40
Customers with neither foreign car nor dog = x%
So that,
30 + 40 + x = 100
70 + x = 100
x = 100 - 70
x = 30
Customers with neither foreign car nor dog = 30.
Converting this value to percentage,
= [tex]\frac{30}{100}[/tex] × 100
= 30%.
Therefore, 30% of his customers have neither a foreign car nor a dog.
The reaction times for a random sample of 9 subjects to a stimulant were recorded as 2.5, 3.6, 3.1, 4.3, 2.9. 2.3, 2.6, 4.1, and 3.4 seconds. Calculate (a) the mean; (b) the median. 8.4 The number of
Answer:
Mean is 3.2
Median is 3.1
Step-by-step explanation:
a) mean
= (2.5+3.6+3.1+4.3+2.9+2.3+2.6+4.1+3.4)/9
= 28.8/9
= 3.2
b) median: we will arrange in ascending order and pick the middle term.
2.3 2.5 2.6 2.9 3.1 3.4 3.6 4.1 4.3
From the above order, 3.1 is the middle term and is the median
a) The mean reaction time of the 9 subjects is 3.2 seconds.
What is a mean?A mean is an average of a set of values.
The mean is computed by summing the values and then dividing the sum by the number of subjects.
b) The median reaction time for the random sample of 9 subjects to a stimulant is 3.1 seconds.
What is the median?The median is the middle number in an arranged list of values. The arrangement takes into consideration their ascending or descending orders.
The median is simple to determine when the list of values is not too long and well-arranged.
Data and Calculations:Variables Reaction Times
in seconds
1. 2.5
2. 3.6
3. 3.1
4. 4.3
5. 2.9
6. 2.3
7. 2.6
8. 4.1
9. 3.4
Total 28.8
Mean = 3.2 (28.8/9)
Determination of the Median:6. 2.3
1. 2.5
7. 2.6
5. 2.9
3. 3.1
9. 3.4
2. 3.6
8. 4.1
4. 4.3
Thus, the mean and the median have been calculated.
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What is the slope of the line that passes through the points (-8, -6) and (-18, 6)
Answer:
Step-by-step explanation:
The mean weekly earnings of a sample of 30 construction workers was $759, with a standard deviation of $73, and the mean weekly earnings of a sample of 28 manufacturing workers was $658, with a standard deviation of $65. Construct a 85% confidence interval for the difference between the mean weekly earnings for construction workers and the mean weekly earnings for manufacturing workers. Round to the second decimal place.
Answer:
[tex] (759-658) -1.46 \sqrt{\frac{73^2}{30} +\frac{65^2}{28}}= 74.54[/tex]
[tex] (759-658) +1.46 \sqrt{\frac{73^2}{30} +\frac{65^2}{28}}= 127.46[/tex]
And the confidence interval for the difference of the two means is given by (74.54, 127.46)
Step-by-step explanation:
Information given:
[tex]\bar X_1 = 759[/tex] the sample mean for construction workers
[tex] s_1 =73[/tex] the sample standard deviation for construction workers
[tex]n_1 =30[/tex] sample size of construction workers
[tex]\bar X_2 = 658[/tex] the sample mean for manufacturing workers
[tex] s_2 =65[/tex] the sample standard deviation for manufacturing workers
[tex]n_2 =28[/tex] sample size of construction workers
Confidence interval
The confidence interval for the difference of means are given by:
[tex] (\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}[/tex]
We need to find the degrees of freedom given by:
[tex] df = n_1 +n_2 -2= 30+28-2=56[/tex]
The confidence is 0.85 and the significance level would be [tex]1-0.85=0.15[/tex] and [tex]\alpha/2 = 0.075[/tex]. We need to find a critical value in the t distribution who accumulates 0.075 of the area on each tail and we got:
[tex] t_{\alpha/2}= \pm 1.46[/tex]
And then we can replace and we got:
[tex] (759-658) -1.46 \sqrt{\frac{73^2}{30} +\frac{65^2}{28}}= 74.54[/tex]
[tex] (759-658) +1.46 \sqrt{\frac{73^2}{30} +\frac{65^2}{28}}= 127.46[/tex]
And the confidence interval for the difference of the two means is given by (74.54, 127.46)
Part (a): The 80% confidence interval for the earnings difference is $77.51 to $124.49.
Part (b): The interval suggests 80% confidence in the true earnings difference falling within $77.51 to $124.49.
Part (c): Since zero isn't in the interval, there's a significant pay difference between construction and manufacturing workers.
Part (a): Construct an 80% confidence interval for the difference between the mean weekly earnings
Step 1: Identify the given data
- Construction workers:
- Mean [tex](\(\bar{X_1}\)) = \$759[/tex]
- Standard deviation [tex](\(s_1\)) = \$73[/tex]
- Sample size [tex](\(n_1\))[/tex] = 30
- Manufacturing workers:
- Mean [tex](\(\bar{X_2}\)) = \$658[/tex]
- Standard deviation [tex](\(s_2\)) = \$65[/tex]
- Sample size [tex](\(n_2\)) = 28[/tex]
Step 2: Determine the formula for the confidence interval
We use the formula for the confidence interval of the difference between two independent means:
[tex]\[ (\bar{X_1} - \bar{X_2}) \pm t_{\alpha/2} \cdot \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} \][/tex]
Step 3: Calculate the standard error (SE) of the difference
[tex]\[ SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} \][/tex]
[tex]\[ SE = \sqrt{\frac{73^2}{30} + \frac{65^2}{28}} \][/tex]
[tex]\[ SE = \sqrt{\frac{5329}{30} + \frac{4225}{28}} \][/tex]
[tex]\[ SE = \sqrt{177.63 + 150.89} \][/tex]
[tex]\[ SE = \sqrt{328.52} \approx 18.12 \][/tex]
Step 4: Determine the degrees of freedom (df) using the Welch-Satterthwaite equation
[tex]\[ df = \frac{\left(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}\right)^2}{\frac{\left(\frac{s_1^2}{n_1}\right)^2}{n_1-1} + \frac{\left(\frac{s_2^2}{n_2}\right)^2}{n_2-1}} \][/tex]
[tex]\[ df \approx \frac{328.52^2}{\frac{(177.63)^2}{29} + \frac{(150.89)^2}{27}} \][/tex]
[tex]\[ df \approx \frac{107,922.4}{1090.15 + 843.48} \][/tex]
[tex]\[ df \approx \frac{107,922.4}{1933.63} \approx 55.83 \approx 56 \][/tex]
Step 5: Find the t-value for an 80% confidence interval
For df ≈ 56 and [tex]\(\alpha/2 = 0.10\),[/tex] the t-value [tex](\(t_{0.10}\))[/tex] is approximately 1.296.
Step 6: Construct the confidence interval
[tex]\[ (\bar{X_1} - \bar{X_2}) \pm t_{\alpha/2} \cdot SE \][/tex]
[tex]\[ (759 - 658) \pm 1.296 \cdot 18.12 \][/tex]
[tex]\[ 101 \pm 23.49 \][/tex]
[tex]\[ (77.51, 124.49) \][/tex]
So, the 80% confidence interval for the difference between the mean weekly earnings is [tex]\((77.51, 124.49)\).[/tex]
Part (b): Explanation of the Confidence Interval
The 80% confidence interval [tex]\((77.51, 124.49)\)[/tex] means that we are 80% confident that the true difference between the mean weekly earnings of construction workers and manufacturing workers lies between [tex]\$77.51[/tex] and [tex]\$124.49[/tex]. In other words, if we were to take many samples and compute the confidence interval for each, about 80% of those intervals would contain the true difference in mean earnings.
Part (c): Is there a significant difference in pay?
To determine if there is a significant difference in pay, we look at whether the confidence interval includes zero. Since the 80% confidence interval for the difference in mean earnings (\(77.51, 124.49\)) does not include zero, we can conclude that there is a statistically significant difference in pay between construction workers and manufacturing workers at the 80% confidence level.
Complete Question:
Solve the equation for x, and enter your answer below.
7 x -5= 65
x=10
Step-by-step explanation:
7x - 5=65
+5 +5 so the 5's cancel so add 5 to 65
7x =70 because you add 5 to 65 to get 70
7x 7
7 x cancels out so you answer will be
x=10
Answer:
x = 10Step-by-step explanation:
7 x -5 = 65
7 times what? (x) - 5 equals 65
Well we know that x has to be less than 65 and more than 7 and -5.
So 7 must be multiplied by numbers 8, and up.
7 * 8 -5 = 51, NOT 65.
7 * 9 -5 = 58, NOT 65.
7 * 10 -5 = Does equal 65.
Therefore, x is equivalent to 10.
What is the surface area of a square pyramid with a slant height of 6cm and the length of one side of the square base is 5cm
Answer:
S = 85cm^2
Step-by-step explanation:
The surface area of a square pyramid is given by the following formula:
[tex]S=2hb+b^2[/tex]
where it has taken into account the sum of the area of a square and four triangles:
[tex]4(\frac{hb}{2})+b*b=2bh+b^2[/tex]
h: slant height = 6cm
b: base = 5cm
By replacing in the formula you obtain:
[tex]S=2(5cm)(6cm)+(5cm)^2=85cm^2[/tex]
hence, the surface area is 85cm^2
A company mixes pecans, cashews, peanuts, and walnuts to make a batch of mixed nuts.
About 15.4% of the mixed nuts in a batch are pecans.
If a batch contains 77 pounds of pecans, how many pounds of mixed nuts are in a batch altogether?
Step-by-step explanation:
15.4% of the nuts are pecans.
0.154x = 77
x = 500
There are 500 pounds of mixed nuts in the batch.
Suppose that 60% of employees at a particular corporation participate in the optional retirement plan. If a random sample of 50 employees is selected, what is the probability that at least 25 employees in the sample will participate in the optional retirement plan?
Answer:
94.41% probability that at least 25 employees in the sample will participate in the optional retirement plan
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 50, p = 0.6[/tex]
So
[tex]\mu = E(X) = np = 50*0.6 = 30[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{50*0.6*0.4} = 3.46[/tex]
What is the probability that at least 25 employees in the sample will participate in the optional retirement plan?
Using continuity correction, this is [tex]P(X \geq 25 - 0.5) = P(X \geq 24.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 24.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24.5 - 30}{3.46}[/tex]
[tex]Z = -1.59[/tex]
[tex]Z = -1.59[/tex] has a pvalue of 0.0559
1 - 0.0559 = 0.9441
94.41% probability that at least 25 employees in the sample will participate in the optional retirement plan
A cylinder with height 2x is inscribed in a sphere with radius 8 meters. The center of the sphere is the midpoint of the altitude that joins the centers of the bases of the cylinder. What is the volume of the cylinder? *
The volume of the cylinder is 401.92 cube m.
Step-by-step explanation:
Given,
A cylinder of height 2x inscribed in a sphere of radius 8 m.
The center of the sphere is the midpoint of the altitude that joins the centers of the bases of the cylinder.
To find the volume of the cylinder.
Formula
The volume of a cylinder with h as height and r as radius is = πr²h
Since,
The cylinder is inscribed in the sphere
The radius (r) of the cylinder = 4 m
The height (h) of the cylinder = 8 m
So,
The volume of the cylinder = π×4²×8 cube m
= 128π cube m [ taking π=3.14]
= 128×3.14 cube m
= 401.92 cube m
Hence,
The volume of the cylinder is 401.92 cube m.
The volume of the cylinder is 128πx.
Explanation:The volume of a cylinder can be found using the formula V = πr²h, where r is the radius of the cylinder's base and h is the height of the cylinder. In this case, the cylinder is inscribed in a sphere with radius 8 meters and the center of the sphere is the midpoint of the altitude that joins the centers of the bases of the cylinder. Since the cylinder is inscribed in the sphere, the diameter of the cylinder is equal to the diameter of the sphere, which is twice the radius of the sphere. Thus, the diameter of the cylinder is 16 meters and the radius is 8 meters.
Since the height of the cylinder is given as 2x, we can substitute this value into the formula to find the volume:
V = π(8)²(2x) = 128πx
Therefore, the volume of the cylinder is 128πx.