Answer:
By the Empirical Rule, in 99.7% of the games that Aubree bowls she scores between 148 and 232
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 190
Standard deviation = 14
Using the empirical rule, what percentage of the games that Aubree bowls does she score between 148 and 232?
148 = 190 - 3*14
So 148 is 3 standard deviations below the mean.
232 = 190 + 3*14
So 232 is 3 standard deviations above the mean
By the Empirical Rule, in 99.7% of the games that Aubree bowls she scores between 148 and 232
Mike weights 200 pounds and plans to lose 1.5 pounds a week, Jeff weights 180 pounds and plans to lose 0.5 pounds a week. When will mike and Jeff weigh the same
Which is the graph of a logarithmic function?
On a coordinate plane, a parabola is shown.
On a coordinate plane, a function is shown. It approaches the x-axis in quadrant 2 and then increases into quadrant 1. It goes through (0, 1) and (1, 2).
On a coordinate plane, a function is shown. It approaches the y-axis in quadrant 4 and approaches y = 2 in quadrant 1. It goes through (1, 0) and (3, 1).
On a coordinate plane, a hyperbola is shown.
Answer:
the third one
Step-by-step explanation:
you can cross out parabola and hyperbola. the second graph is an exponential function because exponential functions go through (0,1), While logarithmic functions go through (1,0).
Answer:
Option 3
Step-by-step explanation:
Edge 2021
An infinite geometric series converges if the common ratio is
An infinite geometric series would only converge if the common ratio is a proper fraction.
What is an infinite geometric series?An infinite geometric series can be defined as the sum of a geometric sequence that typically has a constant common ratio between successive terms but no last term.
In Mathematics, it is a fact that if the common ratio of an infinite geometric series is a proper fraction, this would make it to converge because each successive term gets smaller and smaller.
In conclusion, an infinite geometric series would only converge if the common ratio is a proper fraction such as 3/6.
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Answer:
c. a proper fraction
b and d. -2/3 and 3/4
c. 80/3
Step-by-step explanation:
...
FInd the measure of RST.
Monique ran in a 5-kilometer rece. How many meters did Monique run?
Answer:5000
Step-by-step explanation:
A kilometer is equal to 1000 meters.
5*1000=5000.
Answer:
5000 meters
Step-by-step explanation:
It is given that Monique ran in a 5 kilometer race.
1. The flag-down fare of a taxi is $3.
a. Given that the passenger is charged $0.50 for each kilometer the taxi travels, find the amount of money the passenger has to pay if the taxi covers a distance of
(i) 3 km
(ii) 6 km
(iii) 10 km
b. Given that $y represents the amount of money a passenger has to pay if the taxi travels x km, copy and complete the table.
x 3 6 10
y
Answer:
3 x 0.50=1.5
6 x 0.50=3
10 x 0.50=5
Step-by-step explanation:
x 3, 6, 10
y 1.5, 3, 5
The charges are
For 3 Km the charges would be is $1.5
For 6 Km the charges would be is $3
For 10 Km the charges would be is $5
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
The passenger is charged $0.50 for each kilometer
For 3 Km the charges would be
=3 x 0.50
= $1.5
For 6 Km the charges would be
= 6 x 0.50
=$3
For 10 Km the charges would be
= 10 x 0.50
=$5
The complete Table is
x 3, 6, 10
y 1.5, 3, 5
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In ΔWXY, the measure of ∠Y=90°, XW = 25, YX = 24, and WY = 7. What is the value of the cosine of ∠W to the nearest hundredth?
Answer:
7/25
Step-by-step explanation:
Just did on delta math
According to a Pew Research Center, in May 2011, 35% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students.
She selects 300 community college students at random and finds that 120 of them have a smart phone. In testing the hypotheses: H0: p = 0.35 versus Ha: p > 0.35, she calculates the test statistic as Z = 1.82.
Use the Normal Table to help answer the p-value part of this question.
Click here to access the normal table.
1. There is enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).
2. There is enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.068).
3. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.966).
4. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).
Answer:
[tex]p_v =P(z>1.82)=0.034[/tex]
Assuming a standard significance level of [tex]\alpha=0.05[/tex] the best conclusion for this case would be:
4. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).
Because [tex] p_v <\alpha[/tex]
If we select a significance level lower than 0.034 then the conclusion would change.
Step-by-step explanation:
Data given
n=300 represent the random sample taken
X=120 represent the people who have a smart phone
[tex]\hat p=\frac{120}{300}=0.4[/tex] estimated proportion of people who have a smart phone
[tex]p_o=0.35[/tex] is the value that we want to test
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
System of hypothesis
We need to conduct a hypothesis in order to test the claim that the true proportion of people who have a smart phone is higher than 0.35, the system of hypothesis are.:
Null hypothesis:[tex]p\leq 0.35[/tex]
Alternative hypothesis:[tex]p > 0.35[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.4 -0.35}{\sqrt{\frac{0.35(1-0.35)}{300}}}=1.82[/tex]
Statistical decision
Since is a right tailed test the p value would be:
[tex]p_v =P(z>1.82)=0.034[/tex]
Assuming a standard significance level of [tex]\alpha=0.05[/tex] the best conclusion for this case would be:
4. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).
Because [tex] p_v <\alpha[/tex]
If we select a significance level lower than 0.034 then the conclusion would change.
Use mental math to find the sum of 43 and 57
Answer:
100
Step-by-step explanation:
43+57=100
I added 3+7=10
Then 40+50=90 and added them
90+10=100
Answer: 100
Step-by-step explanation:
You know that 3+7=10
You know that 40+50=90
90+10=100
Now suppose that out of the 10 dishes that the restaurant offers, only 3 of them are vegetarian. If Fiona must select a vegetarian option on Friday, how many ways are there for her to select her lunches?
Answer:
The number of ways she can select her lunches N ;
N = 10×10×10×10×3 = 30000 ways
Step-by-step explanation:
Number of week days = 5
Total number of dishes = 10
Number of vegetarian dishes = 3
Note; on other week days apart from Friday she can select any lunch she want vegetarian or not...
Therefore, on Monday to Thursday she has ten choices per day, and on Friday she has 3 choices
The number of ways she can select her lunches N ;
N = 10×10×10×10×3 = 30000 ways
Explaining What Causes Seasons
Which factors cause Earth to experience seasons? Check all that apply.
the speed of Earth’s rotation
the tilt of Earth’s axis
the directness of the Sun’s rays
the distance from the Sun
the distance from the equator
the altitude of an area
Answer:
The factors that cause Earth to experience seasons are:
1. the tilt of Earth’s axis
2. the directness of the Sun’s rays
The factors that cause Earth to experience seasons are:
1. the tilt of Earth’s axis
2. the directness of the Sun’s rays
Factors that result in the earth experiencing the seasons should be:The reason why the Earth contains various seasons because it deals with the variation of the sun's rays angles and the earth titles to the 23.5 degrees on its axis. Also along with the earth rotation, the earth orbits should be around to the sun because of which various parts should be exposed to the different amount of lights
Therefore, the above two points should be considered.
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The thumb length of fully grown females of a certain type of frog is normally distributed with a mean of 8.59 mm and a standard deviation of 0.63 mm. Calculate the probability that a randomly selected frog of this type has thumb length longer than 9.08 mm.
Answer:
21.77% probability that a randomly selected frog of this type has thumb length longer than 9.08 mm.
Step-by-step explanation:
Problems of normally distributed samples are 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.
In this problem, we have that:
[tex]\mu = 8.59, \sigma = 0.63[/tex]
Calculate the probability that a randomly selected frog of this type has thumb length longer than 9.08 mm.
This is 1 subtracted by the pvalue of Z when X = 9.08. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{9.08 - 8.59}{0.63}[/tex]
[tex]Z = 0.78[/tex]
[tex]Z = 0.78[/tex] has a pvalue of 0.7823
1 - 0.7823 = 0.2177
21.77% probability that a randomly selected frog of this type has thumb length longer than 9.08 mm.
What is the approximate circumference of the circle shown below
Answer:
147.58 cm
Step-by-step explanation:
Circumference is represented by 2πr.
R is 23.5, and I'll approximate π to 3.14, as is common.
This creates 2 • 3.14 • 23.5
Simplify to: 147.58, which is your circumference
Answer:
148
Step-by-step explanation:
To find the circumference, use 2r*3.14 for a approximate answer. in this case, 23.5*2=47.
47*3.14=147.58.
Rounded to the nearest whole number, the answer is 148.
(1 point) A computer retail store has 8 personal computers in stock. A buyer wants to purchase 4 of them. Unknown to either the retail store or the buyer, 4 of the computers in stock have defective hard drives. Assume that the computers are selected at random. (a) In how many different ways can the 4 computers be chosen
Answer:
Total no of different ways can the 4 computers be chosen = 70
Step-by-step explanation:
Given -
A computer retail store has 8 personal computers in stock.A buyer wants to purchase 4 of them.
(Using the combination formula)
The combination of n events taking r at a time = [tex]\mathbf{\binom{n}{r}}[/tex]
where n = 8 and r = 4
Total no of different ways can the 4 computers be chosen = [tex]\mathbf{\binom{8}{4}}[/tex]
= [tex]\boldsymbol{\frac{8!}{(4!)(4!)}}[/tex]
= 70
The number of different ways that 4 computers can be chosen from a stock of 8 is 70.
Explanation:The number of different ways that 4 computers can be chosen from a stock of 8 is determined by the concept of combinations. In this case, we want to find the number of combinations of 8 items taken 4 at a time. The formula for combinations is given by:
C(n, r) = n! / r!(n-r)!
where n is the total number of items and r is the number of items to be chosen. Applying the formula to this problem, we have:
C(8, 4) = 8! / 4!(8-4)!
Simplifying the expression, we get:
C(8, 4) = 8! / 4!4!
Using the factorial function, we can compute:
C(8, 4) = 8 × 7 × 6 × 5 / (4 × 3 × 2 × 1)
C(8, 4) = 70
Therefore, there are 70 different ways that the 4 computers can be chosen from the stock of 8.
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Please help numbers 2-20 evens only
Answer:
clearing picture
Step-by-step explanation:
In the data set below, what are the lower quartile, the median, and the upper quartile?
2,2,2,4,5,6
Lower Quartile: 2
Upper Quartile: 5.25
Median: 3
Final answer:
In the given data set 2, 2, 2, 4, 5, 6, the lower quartile is 2, the median is 3, and the upper quartile is 5.
Explanation:
To find the lower quartile, median, and upper quartile of the given data set 2, 2, 2, 4, 5, 6, we first need to organize it in ascending order, which is already done. Next, we compute the median, which is the middle value when the data set is listed in order. Since there are six numbers, the median will be the average of the third and fourth numbers, (2+4)/2, which is 3.
To find the first quartile (Q1) or lower quartile, we take the median of the lower half of the data set, not including the median. This would be the median of the first three numbers: 2, 2, and 2, which is simply 2. To find the third quartile (Q3) or upper quartile, we look at the upper half of the data set, again not including the median. The median of the last three numbers 4, 5, and 6 is 5.
Therefore, the lower quartile is 2, the median is 3, and the upper quartile is 5.
A diver dives from a cliff with a height of 144 feet. His height, h, in feet is given by the equation h=-16t^2+144 , where t is the time in seconds the diver has fallen. How many seconds will it take for the diver to reach the water?
Answer:
It takes 3 seconds for the diver to reach the water.
Step-by-step explanation:
The height, in feet, is given by the following equation:
[tex]h(t) = -16t^{2} + 144[/tex]
How many seconds will it take for the diver to reach the water?
He reaches the water when his height is 0, that is, when h(t) = 0. So
[tex]h(t) = -16t^{2} + 144[/tex]
[tex]0 = -16t^{2} + 144[/tex]
[tex]16t^{2} = 144[/tex]
[tex]t^{2} = \frac{144}{16}[/tex]
[tex]t^{2} = 9[/tex]
[tex]t = \pm \sqrt{9}[/tex]
[tex]t = \pm 3[/tex]
There are no negative instant of time, so just t = 3.
It takes 3 seconds for the diver to reach the water.
find the area of the polygons 5 cm 5 cm 8 cm square centimeters
Answer:
Answer: 600
Step-by-step explanation:
5x5=25
3x8=24
25x24=600
which point represent on the number line -3/2
Answer:
Half way in between negative 1 and negative 2.
Step-by-step explanation:
4)
I
You deposit $2500 in an account that pays 6 percent annual interest. Find the balance after 3
years if the interest is compounded with the given frequency.
Answer:
$2,977.54
Step-by-step explanation:
You are going to use the compound interest formula:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
P = initial balance
r = interest rate
n = number of times compounded annually
t = time
First, change 6% into the decimal form:
6% -> [tex]\frac{6}{100}[/tex] -> 0.06
Next, lets plug in the values:
[tex]A=2,500(1+\frac{0.06}{1} )^{3(1)}[/tex]
[tex]A=2,977.54[/tex]
Your answer will be $2,977.54
Coralee invests $5,000 in an account that compounds interest monthly and earns 7%. How long will it take her money to double?
Answer:
It will take 10 years for her money to double.
Step-by-step explanation:
The compound interest formula is given by:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the number of years the money is invested or borrowed for.
In this exercise:
We want to find t for which the money doubles, that is, t when A = 2P.
Compounded monthly, an year has 12 months, so n = 12
Interest rate of 7%, so r = 0.07.
The following logarithm property is used:
[tex]\log{a^{t}} = t\log{a}[/tex]
So
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]2P = P(1 + \frac{0.07}{12})^{12t}[/tex]
[tex](1.0058)^{12t} = 2[/tex]
[tex]\log{(1.0058)^{12t}} = \log{2}[/tex]
[tex]12t\log{1.0058} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{12\log{1.0058}}[/tex]
[tex]t = 10[/tex]
It will take 10 years for her money to double.
An e-commerce research company claims that 60% or more graduate students have bought merchandise on-line at their site. A consumer group is suspicious of the claim and thinks that the proportion is lower than 60%. A random sample of 80 graduate students show that only 44 students have ever done so. Is there enough evidence to show that the true proportion is lower than 60%? Assume that significance level of 0.05. Use the hypothesis testing template provided.'
Answer:
We accept H₀ we don´t have enough evidence to conclude that a consumer group position is correct
Step-by-step explanation:
We have a case of test of proportion, as a consumer group is suspicious of the claim and think the proportion is lower we must develop a one tail test (left tail) Then
1.- Test hypothesis:
Null hypothesis H₀ P = P₀
Alternative hypothesis Hₐ P < P₀
2.- At significance level of α = 0,05 Critical value
z(c) = -1,64
3.-We compute z(s) value as:
z(s) = ( P - P₀ )/ √P*Q/n where P = 44/80 P = 0,55 and Q = 0,45
P₀ = 0,6 and n = 80
Plugging all these values in the equation we get:
z(s) = ( 0,55 - 0,6 ) / √(0,2475/80)
z(s) = - 0,05/ √0,0031
z(s) = - 0,05/0,056
z(s) = - 0,8928
4.-We compare z(s) and z(c)
z(s) > z(c) -0,8928 on the left side it means that z(s) is in the acceptance region so we accept H₀
A 64-ounce bottle of
orange juice hos 48 ounces of water, which juice has a greater percent of water
What percent of the bottle of apple juice is water
% water
% water
40
Answer:
Orange juice bottle has greater percent of water.
Percent of water in apple juice bottle=40%
Step-by-step explanation:
We are given that
Total mass of apple juice bottle=80 ounce
Apple juice contains water=32 ounces
Total mass of orange juice bottle=64 ounce
Orange juice bottle contain water=48 ounces
We have to find that which juice has greater percent of water and find the percent of water in the bottle of apple juice .
Percent of water in apple juice=[tex]\frac{water}{total\;mass}\times 100=\frac{32}{80}\times 100=[/tex]40%
Percent of water in orange juice bottle=[tex]\frac{48}{64}\times 100=[/tex]75%
Orange juice bottle has greater percent of water.
Hey, I need help! 2+2+=?
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
Ron wants to calculate the sales tax on two items. He is purchasing a helmet for $42 and gloves for $5.65. Sales tax is 7%. Which expression shows how Ron should calculate his total sales tax?
A
$42 + $5.65 x 7
B
$42 + $5.65 x 0.7
C
($42 + $5.65) x 0.7
D
($42 + $5.65) x 0.07
Last month, Ginger's hotel ran an occupancy rate of 85%. Her competitive set had 150,000 room nights included within it that were available for sale during that month. During that month, the competitive set sold a total of 115,000 rooms. What was the approximate occupancy rate INDEX last month for Ginger's hotel? It's one of the following answer; 78%, 92%, 87% or 39%? Provide details.
Given Information:
Occupancy rate of Ginger’s hotel = 85%
Competitive set available rooms = 150,000
Competitive set sold rooms = 115,000
Required Information:
Occupancy rate INDEX = ?
Answer:
Occupancy rate INDEX = 111%
Step-by-step explanation:
The occupancy rate INDEX is given by
Occupancy rate INDEX = Occupancy rate of Ginger’s hotel/Occupancy rate of competitive set
We are given the occupancy rate of Ginger’s hotel so we need to first find out occupancy rate of competitive set which is given by
Occupancy rate of competitive set = Competitive set sold rooms/Competitive set available rooms
Occupancy rate of competitive set = 115,000/150,000
Occupancy rate of competitive set = 0.7667
Occupancy rate of competitive set ≈ 76.67%
Finally, we can now find the occupancy rate INDEX
Occupancy rate INDEX = Occupancy rate of Ginger’s hotel/Occupancy rate of competitive set
Occupancy rate INDEX = 85/76.67
Occupancy rate INDEX = 1.108
Occupancy rate INDEX = 110.8%
Occupancy rate INDEX ≈ 111%
Therefore, the approximate occupancy rate INDEX last month for Ginger's hotel is 111%
7. (Sec. 7.2) In a survey of 2004 American adults, 501 of them said that they believed in astrology. (a) Calculate and interpret a confidence interval at the 95% confidence level for the proportion of all adult American adults who believe in astrology. (b) Calculate and interpret a 95% lower confidence bound for the proportion of all adult American adults who believe in astrology.
Find the given attachments for complete answer
Answer:
The 95% confidence interval for the proportion for the American adults who believed in astrology is (0.23, 0.27).
This means that we can claim with 95% confidence that the true proportion of all American adults who believed in astrology is within 0.23 and 0.27.
Step-by-step explanation:
We have to construct a 95% confidence interval for the proportion.
The sample proportion is p=0.25.
[tex]p=X/n=501/2004=0.25[/tex]
The standard deviation can be calculated as:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.25*0.75}{2004}}=\sqrt{ 0.000094 }=0.01[/tex]
For a 95% confidence interval, the critical value of z is z=1.96.
The margin of error can be calculated as:
[tex]E=z\cdot \sigma_p=1.96*0.01=0.0196[/tex]
Then, the lower and upper bounds of the confidence interval can be calculated as:
[tex]LL=p-E=0.25-0.0196=0.2304\approx0.23\\\\UL=p+E=0.25+0.0196=0.2696\approx 0.27[/tex]
The 95% confidence interval for the proportion for the American adults who believed in astrology is (0.23, 0.27).
This means that we can claim with 95% confidence that the true proportion of all American adults who believed in astrology is within 0.23 and 0.27.
A sample of 90 women is obtained, and their heights (in inches) and pulse rates (in beats per minute) are measured. The linear correlation coefficient is 0.284 and the equation of the regression line is ModifyingAbove y with caret equals 18.4 plus 0.930 x, where x represents height. The mean of the 90 heights is 63.4 in and the mean of the 90 pulse rates is 77.9 beats per minute. Find the best predicted pulse rate of a woman who is 66 in tall. Use a significance level of alpha equals 0.01.
The best-predicted pulse rate for a woman who is 66 inches tall, using the given regression equation 18.4 + 0.930x, is approximately 79.78 beats per minute.
To predict the pulse rate of a woman who is 66 inches tall using the given regression equation, we plug in the height (x = 66) into the equation:
ModifyingAbove y with caret = 18.4 + 0.930x
Substituting x = 66:
ModifyingAbove y with caret = 18.4 + 0.930(66)
Perform the calculation:
ModifyingAbove y with caret = 18.4 + 61.38
ModifyingAbove y with caret = 79.78
Therefore, the best-predicted pulse rate for a woman who is 66 inches tall is approximately 79.78 beats per minute. This prediction assumes that the relationship between height and pulse rate holds for this particular height value.
At the Canada Open Tennis Championship, a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 99 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph.
If nothing is known about the shape of the distribution, give an interval that will contain the speeds of at least eight-ninths of the player's serves.
a) 54 mph to 144 mph
b) 39 mph to 159 mph
c) 144 mph to 189 mph
d) 69 mph to 129 mph
Answer:
a) 54 mph to 144 mph
Step-by-step explanation:
We don't know the shape of the distribution, so we use Chebyshev's Theorem to solve this question. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
At least eight-ninths of the player's serves.
8/9 is approximately 89%
So
Mean: 99, standard deviation: 15
99 - 3*15 = 54
99 + 3*15 = 144
So the correct answer is:
a) 54 mph to 144 mph
A bottler of drinking water fills plastic bottles with a mean volume of 1,000 milliliters (mL) and standard deviation The fill volumes are normally distributed. What proportion of bottles have volumes greater than
Answer:
84.13% of bottles will have volume greater than 994 mL
Step-by-step explanation:
Mean volume = u = 1000
Standard deviation = [tex]\sigma[/tex] = 6
We need to find the proportion of bottles with volume greater than 994. So our test value is 994. i.e.
x = 994
Since the data is normally distributed we will use the concept of z-score to find the required proportion. First we convert 994 to its equivalent z-score, then using the z-table we will find the corresponding value of proportion. The formula to calculate the z score is:
[tex]z=\frac{x-u}{\sigma}[/tex]
Substituting the values, we get:
[tex]z=\frac{994-1000}{6}=-1[/tex]
This means 994 is equivalent to a z score of -1. Now we will find the proportion of z values which are greater than -1 from the z table.
i.e. P(z > -1)
From the z-table this value comes out to be:
P(z >- 1) = 1 - P(z < -1) = 1 - 0.1587 = 0.8413
Since, 994 is equivalent to a z score of -1, we can write that proportion of values which will be greater than 994 would be:
P( X > 994 ) = P( z > -1 ) = 0.8413 = 84.13%
To find the proportion of bottles with more than 994 mL, calculate the z-score and use a z-table. Approximately 93.32% of bottles are filled with more than 994 mL.
Explanation:To determine the proportion of bottles with volumes greater than 994 mL, we need to use the properties of the standard normal distribution. The mean volume of a bottle is given as 1000 mL with a standard deviation of 4 mL. We first calculate the z-score for 994 mL, which is the number of standard deviations 994 mL is from the mean.
Z = (X - μ) / σ = (994 mL - 1000 mL) / 4 mL = -1.5
Using a z-table or standard normal distribution calculator, we can find the proportion of the area to the right of z = -1.5, which represents the proportion of bottles filled with more than 994 mL. The area to the right of z = -1.5 is approximately 0.9332. Therefore, about 93.32% of the bottles are expected to have volumes greater than 994 mL.