The dingram shows a spinner innde up of a picce of card in the shape of a regular pentagon, with a toothpick pushed through its ceuter. The five triangles are mambered from I to 5. Each time. the spner is spin atil it lands on one of the five edges of the pentagon. The spinener is spun five tinmes. Use the binomial probability formula to enleulate the probability of at most three 4'sThe ratio of boys to girts at birth in Singapore is quite high at 1.09:1 What proportion of Singapore families with exactly 6 children will have at least 3 boys? (ignore the probability of multiple births) what is the answer?
Answers
Answer:
a) [tex]P(X \leq 3) = 0.99328[/tex]
b) 0.6957
Step-by-step explanation:
Let X represent the number of 4's when n = 5 independent spins
each has a probability of 0.2 (i.e p = 0.2)
This notation is represented as:
X [tex]\approx[/tex] Binomial (n = 5, p = 0.2)
Probability of [tex]x[/tex] number of 4's is:
[tex]P(X=x)= (\left \ n \atop x \right) p^x (1-p)^{(n-x)}[/tex]
here; [tex](\left \ n \atop x \right)[/tex] is the combinatorial expression
[tex](\left \ n \atop x \right)[/tex] = [tex]\frac{n!}{x!(n-x)!}[/tex]
[tex]P(X \leq3), n =5 , p = 0.2[/tex]
[tex]P(X \leq3) = 1-P(X > 3)[/tex]
So; let's first find:
[tex]P(X > 3)[/tex]
[tex]= P(3 <X \leq 5) \\ \\ = P(4 <X \leq 5) \\ \\ = P (X = 4, 5) \\ \\ = P (X=4)+P(X = 5 ) \ \ \ (disjoint \ events)[/tex]
[tex]P(X = 4) =( \left \ {{5} \atop {4}} \right. ) (0.2)^4 (1-0.2)^1 \\ \\ P(X = 4) = 5(0.2)^4(0.8)^1 \\ \\ P(X = 4) = 0.0064[/tex]
[tex]P(X = 5) =( \left \ {{5} \atop {5}} \right. ) (0.2)^5 (1-0.2)^0 \\ \\ P(X = 5) = 5(0.2)^5(0.8)^0 \\ \\ P(X = 5) = 0.00032[/tex]
[tex]P (X=4)+P(X = 5 ) \\ \\ = 0.0064 + 0.00032 = 0.006720 \\ \\ \approx 0.007[/tex]
[tex]P(X > 3 ) = 0.00672 \\ \\ P(X \leq 3) = 1- P(X > = 3 ) \\ \\ =1 - 0.00672 \\ \\ = 0.99328[/tex]
[tex]P(X \leq 3) = 0.99328[/tex]
b)
Given that:
The ratio of boys to girls at birth in Singapore is quite high at 1.09:1
What proportion of Singapore families with exactly 6 children will have at least 3 boys?
Probability of having a boy = [tex]\frac{1.09}{1+1.09}[/tex] = 0.5215
Binomial Problem with n = 6
P(3<= x <=6) = 1 - P(0<= x <=2)
= 1 - binomial (6,0.5215,2)
= 0.6957
Related Questions
Find the point estimate for the true difference between the given population means. Round your answer to three decimal places.
(HINT: The point estimate for the difference between the population means is found by simply subtracting one sample mean from the other.)
Sample 1: Weights (in Grams) of Soap Bar A:
129, 127, 129, 129, 128, 130, 127, 129, 128, 131, 127
_____________________________________________________________
Sample 2: Weights (in Grams) of Soap Bar B:
131, 126, 132, 129, 128, 131, 131, 130, 128, 129, 126, 132, 131
Answers
Answer:
Point Estimate for different between population means = - 0.99
Step-by-step explanation:
We are given data of two samples and we have to find the best point estimate of the true difference between two population means. Remember that in absence of data about population the best estimator is the sample data. So, we will find the means of both sample data and find the difference of that means. This difference between the means of sample data will be the best point estimate for the true difference between the population means.
Formula to calculate the mean is:
[tex]Mean=\frac{\text{Sum of Values}}{\text{Number of Values}}[/tex]
Mean of Sample 1:
[tex]Mean=\frac{1414}{11}=128.55[/tex]
Mean of Sample 2:
[tex]Mean=\frac{1684}{13}=129.54[/tex]
Therefore the best point estimate for difference between two population means would be = Mean of Sample 1 - Mean of Sample 2
= 128.55 - 129.54
= - 0.99
Final answer:
The point estimate for the true difference between the given population means is -1.028.
Explanation:
The point estimate for the true difference between the given population means can be found by subtracting one sample mean from the other. Let's calculate it:
Sample 1: 129, 127, 129, 129, 128, 130, 127, 129, 128, 131, 127
Sample 2: 131, 126, 132, 129, 128, 131, 131, 130, 128, 129, 126, 132, 131
Sample mean of Sample 1 = (129+127+129+129+128+130+127+129+128+131+127)/11 = 128.818
Sample mean of Sample 2 = (131+126+132+129+128+131+131+130+128+129+126+132+131)/13 = 129.846
Point estimate for the difference = Sample mean of Sample 1 - Sample mean of Sample 2 = 128.818 - 129.846 = -1.028
At a certain university, 22% of the students fail general chemistry on their first attempt. Professor Brown teacher at this university and believes that the rate of first-time failure in his general chemistry classes is 45%. He samples 86 students from last semester who were first-time enrollees in general chemistry and finds that 19 of them failed his course.
1) State the appropriate null and alternate hypotheses.
2) Compute the P-value.
3) Using a = 0.05, can Professor Brown conclude that the percentage of failures differs from 45%?
Answers
Answer:
[tex]a. \ H_o:p=0.45, \ \ \ \ H_a:p\neq 0.45\\\\b.\ \hat p=0.2209\\\\c. \ Yes\ (-4.2706<-1.96)[/tex]
Step-by-step explanation:
a. The professor's claim is that 45% first-timers fail his test. The null hypothesis is therefore stated as:
[tex]H_o:p=0.45[/tex]
-The alternative hypothesis is that more or less people fail the test as opposed to the professor's exact claim, hence:
[tex]H_a:p\neq 0.45[/tex]
b. To compute the P-value we use the z-value for a 95% confidence level:
[tex]z_{\alpha/2}=z_{0.025}=1.96[/tex]
#The proportion of failures in the sample of 86 is 19:
[tex]\hat p=\frac{19}{86}\\\\=0.2209[/tex]
The z-value is calculated as:
[tex]z=\frac{\hat p-p_o}{\sqrt{\frac{p_o(1-p_o)}{n}}}[/tex]
[tex]=\frac{0.2209-0.45}{\sqrt{\frac{0.45(1-0.45)}{86}}}\\\\\\=-4.2706[/tex]
-4.2706 is less than the stated confidence level for the given 45% proportion and greatly differs from it.
- Reject the null hypothesis as there is enough evidence to reject the claim.
-Hence,Yes, Professor Brown can conclude that percentage of failures differs from 45%.
A builder makes all of their ramps with a base to height ratio of 12:112:112, colon, 1 to be wheelchair-accessible. See the diagram below, which is not drawn to scale:
A certain ramp needs to cover a height of 0.80.80, point, 8 meters.
What is the length \ellℓell of this ramp?
Round your answer to the nearest hundredth of a meter.
Answers
The length of the L of the ramp, which the builder makes with a base to height ratio of 12 to 1 is 9.63 meter.
Pythagoras theorem states that, right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
A builder makes all the ramps with a base to height ratio of 12 to 1 to be wheelchair accessible.
Let p is the factor of ratio. Thus, the height and base is,
h = p
b = 12p
According to Pythagoras theorem,
unknown side (say l) is hypotenuse
l² = (12p)² + p²
[tex]l^2=144p+p^2[/tex]
[tex]l = \sqrt{144p+p^2}[/tex]
[tex]l = \sqrt{145} p[/tex]
A ramp needs to cover a height of 0.8 m. Height is equal to the factor p.
Thus, the value of p is,
p = h
p = 0.80
Thus, the length of the l is,
[tex]l = \sqrt{145} p[/tex]
[tex]l = \sqrt{145} {(0.8)}[/tex]
[tex]l=(12.041)(0.8)[/tex]
[tex]l=9.63m[/tex]
Hence, the length of the L of the ramp, which the builder makes with a base to height ratio of 12 to 1 is 9.63 meter.
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The correct question has in the image below
The Martin family's truck gets an average of 35 miles per gallon. Predict how many miles they can drive
using 4 gallons of gas.
Answers
Answer:
25 miles per gallon x 7 gallons used=175 miles driven
175/7=25
NOTE: THIS IS AN EXAMPLE
A production process manufactures electronic components with timing signals whose duration follows a normal distribution. A random sample of 55 components was taken, and the durations of their timing signals were measured.a. The probability is 0.01 that the sample variance is bigger than what percentage of the population variance?
b. The probability is 0.05 that the sample variance is less than what percentage of the population variance?
Answers
Answer:
Check the explanation
Step-by-step explanation:
b ) [tex]P(s^2<p\sigma^2)=0.05[/tex]
or , [tex]P\left (\frac{(n-1)s^2}{\sigma^2}<(n-1)p \right )=0.05[/tex]
or , [tex]P\left (\chi^2_5<5p \right )=0.05=P(\chi^2_5< 1.145476 )[/tex]
or , 5p =1.145476
or , [tex]p =\frac{1.145476}{5}= 0.2290952[/tex]
Required percentage = 22.91
Coach Riley needs eight new volleyballs. If the retail price for one ball is $20 at ALL SPORTS and the SPORT SHACK, which store should he buy from in order to pay the least amount? How much will he save?
Answers
Answer:
The way you worded this he should buy at either store because the price is 20 at both and he won't have any savings because they have the same price.
Step-by-step explanation:
Answer:
Well correct me if I am wrong but I think something is missing in this problem because I do not see another number to compare $20 to...
PLEASE HELP !!!! What happens to the value of the expression 20+a20+a20, plus, a as a increases?
Choose 1 answer:
(Choice A)
A
It increases.
(Choice B)
B
It decreases.
(Choice C)
C
It stays the same.
Answers
Answer:
the answer is a it increases
Step-by-step explanation:
Answer:
(A)- It increases
Step-by-step explanation:
Good luck with your unit test for Kahn!!
XYZ has been rotated 90°, as shown in the diagram. What is the length of
Y'Z?
Help Idk the answer
Answers
Answer:
7
Step-by-step explanation:
Identify the domain of the function shown in the graph.
Answers
The domain is all possible values of x, and since the graph seemingly stretches forever, the domain is all real numbers.
In November 2010, an article titled "Frequency of Colds Dramatically Cut with Regular Exercise" appeared in Medical News Today. The article was based on the findings of a study by researchers Nieman et al. (British Journal of Sports Medicine, 2010) that followed 1,002 people aged 18–85 years for 12 weeks, asking them to record their frequency of exercise (5 or more days a week? Yes or No) as well as incidences of upper respiratory tract infections (Cold during last week? Yes or No.)
Answers
Answer:
Part a
For the given study, the explanatory variable or independent variable is given as regularity or frequency of exercise. This variable is classify as categorical variable because variable is divided into two categories such as whether participant exercise 5 or more days a week or not.
Part b
For the given study, the response variable or dependent variable is given as frequency of colds. This variable is classified as quantitative variable because we measure the quantities or frequency of number of colds.
Part c
A confounding variable for this research study is given as incidence of upper respiratory tract infections that provides an alternative explanation for the lower frequency of colds among those who exercised 5 or more days per week, compared to those who were largely sedentary. This confounding variable is categorical in nature.
The angle measures in a triangle are 25°, 135°, and 20°. What type of triangle is it?
acute triangle
right triangle
obtuse triangle
isosceles triangle this is very confusing to me lol
Answers
The type of triangle is,
⇒ A scalene triangle
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The angle measures in a triangle are 25°, 135°, and 20°.
Now, We have alL angles are different to each other.
Hence, By definition of a scalene triangle,
The type of triangle is,
⇒ A scalene triangle
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What do 2+e(6-7)? Everybody is saying it’s 2 but idk
Answers
Answer:
-0.71828
Step-by-step explanation:
2 + e(6-7)
2 + e(-1)
2 -e
e is approximately 2.718281828459045235360287471352662497757247093699959574966
2 - 2.71828.....
-0.71828
Answer:
2.37 (3 sf)
Step-by-step explanation:
2 + e^(6-7)
2 + e^(-1)
2 + 1/e (exact)
Roughly, 2.367879441
Find the volume of this prism.
Image attached
Answers
Answer:
840cm³
Step-by-step explanation:
devide them into 2 shapes.
the shape at the bottoma×b×h
15cm×6cm×8cm=720cm³the shape at the topa×b×h
a: 5 cmb: 6 cmh: 12-8=4 cm5cm×6cm×4cm=120cm³V=720cm³+120cm³=840cm³
Answer:
840 cm^3
Step-by-step explanation:
L x W x H = V
Split the prism into 2 different prisms.
6 is constant throughout the figure, so all we have to do is find the L and H of the two prisms and multiply them by 6.
15 x 8 = 120
The height of the higher prism can be determined by subtracting the bottom height from the total height.
12 - 8 = 4
5 x 4 = 20
Add the two side areas together.
20 + 120 = 140
Multiply by the width, 6.
140 x 6 = 840
The amount of soda in a 16-ounce can is normally distributed with a mean of 16 ounces and a standard deviation of .5 ounce. What is the probability that a randomly selected can will have less than 15.5 ounces? Round your answers to four decimal places.
Answers
Under a normal distribution with a mean of 16 ounces and a standard deviation of 0.5 ounce, there's a 15.87% probability that a randomly selected can will have less than 15.5 ounces of soda.
Explanation:This question is related to probability within the field of statistics. Particularly, it's about the normal distribution, a common statistical distribution that shows the spread of data around the mean. In this specific case, the amount of soda in a 16-ounce can is normally distributed with a mean (µ) of 16 ounces and a standard deviation (σ) of 0.5 ounce.
We're asked to calculate the probability that a randomly selected can will have less than 15.5 ounces. This requires us to standardize the score of 15.5, meaning we use the formula (X - µ) / σ, where X is the value we are assessing. So, (15.5 - 16) / 0.5 equals -1.
This standardized score is known as a z-score, and tells us how many standard deviations a value is from the mean. In this case, 15.5 is one standard deviation below the mean. We then look up this z-score in a z-table, which gives us the probability associated with this z-score. For a z-score of -1, the probability is 0.1587, or 15.87%.
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The probability that a randomly selected can will have less than 15.5 ounces is approximately 0.1587.
To find the probability that a randomly selected can will have less than 15.5 ounces, we can use the standard normal distribution.
First, we need to calculate the z-score for 15.5 ounces using the formula:
[tex]\[ z = \frac{{X - \mu}}{{\sigma}} \][/tex]where:
X is the value we're interested in (15.5 ounces), [tex]\( \mu \)[/tex]is the mean (16 ounces), [tex]\( \sigma \)[/tex] is the standard deviation (0.5 ounce).Plugging in the values:
[tex]\[ z = {{15.5 - 16}}/{{0.5}} \][/tex][tex]\[ z = {{-0.5}}/{{0.5}} \][/tex]z = -1Next, we look up the z-score of -1 in the standard normal distribution table to find the probability. The probability that a randomly selected can will have less than 15.5 ounces is the area to the left of the z-score of -1.
Using the standard normal distribution table, the area to the left of -1 is approximately 0.1587.
Therefore, the probability that a randomly selected can will have less than 15.5 ounces is approximately 0.1587.
The correlation analysis assumes that the measurements have a bivariate normal distribution in the population. Select all of the features that define a bivariate normal distribution.
A) A cloud of points that is funnel shaped (wider at one end than the other)
B) A relationship between X and Y that is not linear
C) The frequency distributions of X and Y separately are normal
D) Either X or Y has a decidedly skewed distribution
E) The presence of outliers Bell-shaped probability distribution in two dimensions rather than one
D) A relationship between X and Y that is linear
Answers
Answer:
Bruh i got correlation hw that i posted on here too and nobody helped lol.
Step-by-step explanation:
A wheel, which is part of a game at a shopping center is arranged to give 2 tickets 50% of the time, 5 tickets 25% of the time, 10 tickets 23% of the time, and 10 tickets 2% of the time. A player enters the shopping center and spins the wheel. Calculate the expected number of tickets he will get.
Answers
Answer:
The expected number of tickets a customer will get is 4.75.
Step-by-step explanation:
The probability distribution of the number of ticket a wheel at a shopping center is arranged to give is as follows:
X Probability (p)
2 0.50
5 0.25
10 0.23
10 0.02
The formula to compute the expected value of a random variable is:
[tex]E(X)=\sum x\cdot P (X=x)[/tex]
Compute the expected number of tickets a customer will get as follows:
[tex]E(X)=\sum x\cdot P (X=x)[/tex]
[tex]=(2\times 0.50)+(5\times 0.25)+(10\times 0.23)+(10\times 0.02)\\=1+1.25+2.3+0.2\\=4.75[/tex]
Thus, the expected number of tickets a customer will get is 4.75.
The sum of 5 fifteens and 3 fifteens
Answers
Answer:
(5 x 15) + (3 x 15) = 120
Step-by-step explanation:
5 x 15 = 75
3 x 15 = 45
75 + 45 = 120
Hope this helps :)
Answer:
5 * 15 = 75
3 * 15 = 45
45 + 75 = 120
Step-by-step explanation:
When you have a equation like that, you need to multiply. It is a faster way to solve the problem.
You had 15 five times.
15+15+15+15+15= 75 It equals the same thing because it is the same as 5 * 15
Same for the three fifteens.
15+15+15= 45.
The sum of the whole equation is 120 because you add 75 and 45.
Hope this helps, have a good day/night. Stay safe and healthy!
The Eastside High School marching band is made up of the instrument players and the percussion. If there are 245 members who play instruments and 35 percussion members, then what percent of the marching band is percussion?
Answers
Answer:
14%
Step-by-step explanation:
you divide 35 by 245 to get 0.14285714285 than you round
A cell phone weighs about 2.8 times 10 Superscript n pounds. Which value of n is most reasonable? Negative 3 Negative 1 0 1
Answers
Answer:
-1
Step-by-step explanation:
The weight of the cell phone is given by:
[tex]W=2.8*10^n[/tex]
The options provided for 'n' are:
a. -3
b. -1
c. 0
d. 1
Applying the possible values:
[tex]W_a=2.8*10^{-3}\\W_a = 0.0028\ pounds\\\\W_b=2.8*10^{-1}\\W_b = 0.28\ pounds\\\\W_c=2.8*10^{0}\\W_c = 2.8\ pounds\\\\W_d=2.8*10^{1}\\W_d = 28\ pounds[/tex]
A cellphone could not possibly weigh as little as 0.0028 or as much as 2.8 or 28 pounds. Therefore, the most reasonable value for n is -1.
Answer:
(B)-1
Step-by-step explanation:
Let us plug in the given values into [tex]2.8X10^n[/tex][tex]2.8X10^{-3}=2.8X 0.001=0.0028\:Pounds\\2.8X10^{-1}=2.8X 0.1=0.28\:Pounds\\2.8X10^{0}=2.8X 1=2.8\:Pounds\\2.8X10^{1}=2.8X 10=28\:Pounds[/tex]
A reasonable value for the weight of a cell phone will be 0.28 Pounds.
Therefore, n=-1
PLEASE HELP!!!!!!Dimensions of the triangular prism
Base - 20 feet by 20 feet
Height - 40 feet
Dimensions of the rectangular prism
Base - 15 feet by 40 feet
Height - 20 feet
What is the total amount of volume inside the parking
garage?
16.000
18.000
24.000
Answers
Answer:20000ft^3
Step-by-step explanation:
volume of triangular prism:
Base area x height
1/2 x 20 x 20 x40
(1x20x20x40) ➗ 2
16000 ➗ 2=8000ft^3
Volume of rectangular prism:
Length x width x height
40 x 15 x 20=12000ft^3
Total volume=8000+12000
Total volume=20000ft^3
The total amount of volume inside the parking garage = 20,000 cu. ft.
What is the volume of the triangular prism?The volume of the triangular prism = base area × height
What is the volume of the rectangular prism?V = l × b × h, where 'l' represents the length, 'w' represents the width and 'h' represents the height of the rectangular prism
For given example,
Let V1 represents the volume of the triangular prism and V2 represents the volume of the rectangular prism.
Dimensions of the triangular prism are:
Base - 20 feet by 20 feet and Height - 40 feet
The base of the triangular prism is a triangle.
So, the area of the base would be,
⇒ A = 1/2 × 20 × 20
⇒ A = 200 sq. ft.
The volume of the triangular prism would be,
⇒ V1 = base area × height
⇒ V1 = 200 × 40
⇒ V1 = 8,000 cubic feet
Now, the dimensions of the rectangular prism are:
Base - 15 feet by 40 feet and Height - 20 feet
⇒ l = 40ft., w = 15 ft., h = 20 ft.
The volume of the rectangular prism would be,
⇒ V2 = l × w × h
⇒ V2 = 40 × 15 × 20
⇒ V2 = 12,000 cu. ft.
So, the total amount of volume inside the parking garage would be,
⇒ V = V1 + V2
⇒ V = 8000 + 12000
⇒ V = 20,000 cu. ft.
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Need help with this
Answers
What is the area of the following shape?
Answers
Answer:
114 square meters
Step-by-step explanation:
formula:1/2×h(a+b)
1/2×12{(12+5)+12}
1/2×12(17+12)
=6×19
=114m^2
This table gives a few (x,y)(x,y)left parenthesis, x, comma, y, right parenthesis pairs of a line in the coordinate plane. -28 -54 -21 -40 -14 -26 What is the y-intercept of the line?
Answers
Answer:
The y-intercept is y = 2
Step-by-step explanation:
A linear function has the following format:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept, which is the value of y when x = 0.
We are given these three points:
(-28, -54)
(-21, -40)
(-14, -26)
We use two of them to build a system, to find values for m and b.
(-28, -54)
This means that when [tex]x = -28, y = -54[/tex]
So
[tex]y = mx + b[/tex]
[tex]-54 = -28m + b[/tex]
[tex]28m = b + 54[/tex]
[tex]m = \frac{b + 54}{28}[/tex]
(-21, -40)
This means that when [tex]x = -21, y = -40[/tex]
So
[tex]y = mx + b[/tex]
[tex]-40 = -21m + b[/tex]
[tex]-40 = -21\frac{b + 54}{28} + b[/tex]
[tex]-40 = \frac{-21b - 1134 + 28b}{28}[/tex]
[tex]7b - 1134 = -40*28[/tex]
[tex]7b = 14[/tex]
[tex]b = \frac{14}{7}[/tex]
[tex]b = 2[/tex]
The y-intercept is y = 2
Answer:
y = (0,2)
Step-by-step explanation:
A manufacturer of a new medication on the market for Parkinson's disease makes a claim that the medication is effective in 75% of people who have the disease. One hundred fifty individuals with Parkinson's disease are given the medication, and 100 of them note the medication was effective. Does this finding provide statistical evidence at the 0.05 level that the effectiveness is less than the 75% claim the company made? Make sure to include parameter, conditions, calculations, and a conclusion in your answer.
Answers
Answer:
Claim is rejected
Step-by-step explanation:
Solution:-
- The claim was made on the effectiveness of medication on the market of Parkinson's disease to be p = 75%.
- A random sample was taken of N = 150 individuals and n = 100 number of people reported that it was effectively.
- We are to test the claim made by the manufacturer of the medication based on the statistics available for the sample N.
- State the hypothesis for the effectiveness of medication:
Null Hypothesis: p = 0.75 ... Claim
Alternate hypothesis: p < 0.75 .... Test
- The conditions of standard normality:
n*p > 5 , 150*0.75 = 112.5 .. ( Check )n*(1-p) > 5 , 150*0.25 = 37.5 .. ( Check )Hence, the standard normal test is applicable. Assuming the population proportion to be normally distributed.
- We will estimate the population proportion with the sample proportion ( p* ):
p* = n / N
p* = 100 / 150
p* = 2/3 = 0.667
- Testing against the claimed population proportion ( p ) = 0.75. The standard normal statistic value is given by:
[tex]Z-test= \frac{(p^* - p)}{\sqrt{p(1-p) / N} } \\\\Z-test= \frac{(0.6667 - 0.75)}{\sqrt{0.75(0.25) / 150} } \\\\Z-test= \frac{-0.0833}{\sqrt{0.00125} } \\\\Z-test= -2.35607 \\[/tex]
- We will see whether the Z-test statistic falls in the rejection region defined by the critical value of Z at significance level ( α ) of 0.05.
- The rejection region is defined by the Alternate hypothesis which is less than the claimed value. So, the rejection region defined by the lower tail of the standard normal.
- So for lower tailed test the critical value of statistics is:
P ( Z < Z-critical ) = α = 0.05
Z-critical = - 1.645
- The rejected values all lie to the left of the Z-critical value -1.645
- The claim test value is compared the rejection region:
-2.35607 < -1.645
Z-test < Z-critical
Hence, Null hypothesis rejected because test lies in the rejection region.
Conclusion:
The Null hypothesis or claim made by the manufacturer of Parkinson's disease medication of 75% effectiveness is without sufficient evidence. Hence, the claim made is false or has no statistical evidence.
By calculating the Z-score and corresponding p-value for the statistical test, we found that there is significant evidence at the 0.05 level to suggest that the medication's effectiveness is less than the 75% claimed.
Explanation:The subject we're dealing with here is hypothesis testing in statistics, where we have a claim (the effectiveness of the medication is 75%) and we are testing whether the observations (effectiveness in 100 out of 150 individuals) support this claim.
Firstly, the parameter of interest here is the proportion (p) of individuals for whom the medication is effective. Our null hypothesis (H0) is that p = 0.75 and our alternate hypothesis (Ha) is that p < 0.75.
To conduct the hypothesis test, let's check the conditions:
Random: It's not mentioned, but assuming these 150 individuals were chosen randomly, this condition is met.Normal: Since both np (150 * 0.75 = 112.5) and n(1-p) (150 * 0.25 = 37.5) are greater than 10, the sampling distribution will be approximately normal.Independent: Again, this is not stated, but let's assume the responses from the individuals are independent.The sample proportion (p-hat) = 100/150 = 0.67
Next, we calculate the Z score, which is (p-hat - p) / sqrt[p(1-p)/n] = (0.67 - 0.75) / sqrt[0.75 * (0.25) / 150] = -1.65. The p-value associated with a Z score of -1.65 is 0.0495.
Since the p-value is less than the significance level of 0.05, we reject H0 and conclude that there is statistically significant evidence at the 0.05 level that the effectiveness of medication is less than 75% as claimed by the manufacturer.
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Determine the simple interest earned on $21,500 after 16 years if the APR is 9 %.
Answers
The student asked about the simple interest earned on an investment. The simple interest can be calculated using the formula I = PRT. For a principal of $21,500 at a 9% APR for 16 years, the interest earned is $30,960.
Explanation:To calculate simple interest, you can use the formula I = PRT, where I is the interest, P is the principal amount (the initial amount of money), R is the rate of interest per period, and T is the time the money is invested for.
In this case, we have:
P (Principal) = $21,500R (Rate) = 9% or 0.09T (Time) = 16 yearsPlugging these values into the formula, we get:
I = PRT
I = $21,500 × 0.09 × 16
I = $30,960
The simple interest earned after 16 years is $30,960.
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Final answer:
The simple interest on $21,500 at 9% APR over 16 years is calculated using the formula I = PRT, which gives us a total interest of $30,960.
Explanation:
To calculate the simple interest earned on a sum of money, we can use the formula I = PRT, where I stands for interest, P for principal amount, R for the annual interest rate (in decimal form), and T for the time in years. In this case, the student wants to determine the interest earned on $21,500 at 9% APR for 16 years.
First, convert the interest rate from a percentage to a decimal by dividing by 100:
R = 9% / 100 = 0.09
Next, apply the values to the simple interest formula:
I = PRT
I = $21,500 × 0.09 × 16
I = $30,960
Therefore, the total simple interest earned after 16 years is $30,960.
Select three ratios that are equivalent to 8:20
A: 1:4
B: 4:10
C: 24:60
D: 2:5
E: 10:24
Answers
Answer:
8 to 20 1 to 4 4 to 10
Step-by-step explanation:
it was easy
Consider the following system of equations. StartLayout Enlarged left-brace 1st row y = 6 x squared 2nd row y = x squared + 4 EndLayout Which statement describes why the system has two solutions? Each graph has one y-intercept, which is a solution. Each graph has one vertex, which is a solution. The graphs of the equations intersect the x-axis at two places. The graphs of the equations intersect each other at two places.
Answers
Answer:
The graphs of the equations intersect each other at two places.
The correct answer is the graphs of the equations intersect each other at two places.
Why does an equation have 2 solutions?A quadratic expression can be written as the product of two linear factors and each factor can be equated to zero, So there exist two solutions.
How do you know if a graph has two solutions?Each shows two lines that make up a system of equations. If the graphs of the equations intersect, then there is one solution that is true for both equations. If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations.
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An angle measures 30° more than the measure of its complementary angle. What is the measure of each angle?
Answers
Angle: [tex]\( 60^\circ \)[/tex], complementary angle: [tex]\( 30^\circ \)[/tex]. Angle is 30° more than its complementary angle.
Let's denote the measure of the angle as [tex]\( x \)[/tex] degrees.
The complementary angle would be [tex]\( 90^\circ - x \)[/tex] degrees.
Given that the angle measures 30° more than its complementary angle, we can write the equation:
[tex]\[ x = (90^\circ - x) + 30^\circ \][/tex]
Now, let's solve for [tex]\( x \)[/tex]:
[tex]\[ x = 90^\circ - x + 30^\circ \][/tex]
[tex]\[ 2x = 90^\circ + 30^\circ \][/tex]
[tex]\[ 2x = 120^\circ \][/tex]
Dividing both sides by 2:
[tex]\[ x = \frac{120^\circ}{2} \][/tex]
[tex]\[ x = 60^\circ \][/tex]
So, the angle measures [tex]\( 60^\circ \)[/tex] and its complementary angle measures:
[tex]\[ 90^\circ - 60^\circ = 30^\circ \][/tex]
Therefore, the measure of the angle is [tex]\( 60^\circ \)[/tex] and the measure of its complementary angle is [tex]\( 30^\circ \)[/tex].
The two graphs below compare the gallons of gasoline used and the total distance traveled for two different cars.
Car 1
A graph has gallons of gasoline used on the x-axis and miles traveled on the y-axis. A line goes through points (2, 50) and (4, 100).
Car 2
A graph has gallons of gasoline used on the x-axis and miles traveled on the y-axis. A line goes through points (2, 40) and (4, 80).
Which comparison of the slopes of the two lines is accurate?
Answers
The comparison of the slopes is accurate: the slope of the line for Car 1 is greater than the slope of the line for Car 2.
Step 1:
The comparison of the slopes of the two lines can be made by calculating the slope of each line. Let's calculate the slopes:
For Car 1:
The coordinates are (2, 50) and (4, 100).
Using the slope formula [tex]\( m = \frac{y_2 - y_1}{x_2 - x_1} \)[/tex]:
[tex]\[ m = \frac{100 - 50}{4 - 2} = \frac{50}{2} = 25 \][/tex]
For Car 2:
The coordinates are (2, 40) and (4, 80).
Using the slope formula:
[tex]\[ m = \frac{80 - 40}{4 - 2} = \frac{40}{2} = 20 \][/tex]
Step 2:
Comparing the slopes:
- The slope of the line for Car 1 is 25.
- The slope of the line for Car 2 is 20.
Therefore, the comparison of the slopes is accurate: the slope of the line for Car 1 is greater than the slope of the line for Car 2.
How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 41 tissues during a cold. Suppose a random sample of 10,000 people yielded the following data on the number of tissues used during a cold: x = 35, s = 18.
Answers
Answer:
7
Step-by-step explanation:
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