According to one study, brain weights of men are normally distributed with a mean of 1.60 kg and a standard deviation of 0.13 kg. Use the data to answer parts (a) through (e). Click here to view page 1 of the table of areas under the standard normal curve. Click here to view page 2 of the table of areas under the standard normal curve, a. Determine the sampling distribution of the sample mean for samples of size 3. Interpret your answer in terms of the distribution of all possible sample mean brain weights for samples of three men. The mean of the sample mean is µ; = 1.1 kg. (Type an integer or a decimal. Do not round.) The standard deviation of the sample mean is o: = 0.0693 kg. (Round to four decimal places as needed.) Interpret these answers in context. For samples of three men, the possible sample mean brain weights have a normal distribution with a mean of 1.1 kg and a standard deviation of 0.0693 kg. (Type integers or decimals rounded to four decimal places as needed.) b. Repeat part (a) for samples of size 12. The mean of the sample mean is u: =|1.1| (Type an integer or a decimal. Do not round.) The standard deviation of the sample mean is o: = 0.0346. (Round to four decimal places as needed.) Interpret these answers in context. For samples of 12 men, the possible sample mean brain weights have a normal distribution with a mean of 1.1 kg and a standard deviation of 0.0346 kg.
According to one study, brain weights of men are normally distributed with a mean of 1.60 kg and a standard deviation of 0.13 kg. Use the data to answer parts (a) through (e). Click here to view page 1 of the table of areas under the standard normal curve. Click here to view page 2 of the table of areas under the standard normal curve, a. Determine the sampling distribution of the sample mean for samples of size 3. Interpret your answer in terms of the distribution of all possible sample mean brain weights for samples of three men. The mean of the sample mean is µ; = 1.1 kg. (Type an integer or a decimal. Do not round.) The standard deviation of the sample mean is o: = 0.0693 kg. (Round to four decimal places as needed.) Interpret these answers in context. For samples of three men, the possible sample mean brain weights have a normal distribution with a mean of 1.1 kg and a standard deviation of 0.0693 kg. (Type integers or decimals rounded to four decimal places as needed.) b. Repeat part (a) for samples of size 12. The mean of the sample mean is u: =|1.1| (Type an integer or a decimal. Do not round.) The standard deviation of the sample mean is o: = 0.0346. (Round to four decimal places as needed.) Interpret these answers in context. For samples of 12 men, the possible sample mean brain weights have a normal distribution with a mean of 1.1 kg and a standard deviation of 0.0346 kg.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Question
Transcribed Image Text:According to one study, brain weights of men are normally distributed with a mean of 1.60 kg and a standard deviation of 0.13 kg. Use the data to answer parts (a) through (e).
Click here to view page 1 of the table of areas under the standard normal curve.
Click here to view page 2 of the table of areas under the standard normal curve.
c. Construct a graph of the normal population distribution and the two sampling distributions for brain weights. Choose the correct graph below.
O A.
В.
С.
OD.
Роp
Pop
n = 12
n = 3
n = 3
n = 12
n = 3
n = 12
n = 12
n = 3
Pop
Роp
1.6
1.6
1.6
1.6
d. Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.60 kg. Interpret your answer in terms of sampling error.
85 %
(Round to two decimal places as needed.)
This is the percentage that the sampling error made in estimating
the mean brain weight of all men
by that of
a sample of three men
will be at most 0.1 kg.
Transcribed Image Text:According to one study, brain weights of men are normally distributed with a mean of 1.60 kg and a standard deviation of 0.13 kg. Use the data to answer parts (a) through (e).
Click here to view page 1 of the table of areas under the standard normal curve.
Click here to view page 2 of the table of areas under the standard normal curve.
a. Determine the sampling distribution of the sample mean for samples of size 3. Interpret your answer in terms of the distribution of all possible sample mean brain weights for samples of three men.
The mean of the sample mean is
= 1.1 kg.
(Type an integer or a decimal. Do not round.)
The standard deviation of the sample mean is o; = 0.0693 kg.
(Round to four decimal places as needed.)
Interpret these answers in context.
For samples of three men, the possible sample mean brain weights have a normal distribution with a mean of 1.1 kg and a standard deviation of 0.0693 kg.
(Type integers or decimals rounded to four decimal places as needed.)
b. Repeat part (a) for samples of size 12.
The mean of the sample mean is
= 1.1
(Type an integer or a decimal. Do not round.)
The standard deviation of the sample mean is o; = 0.0346
X
(Round to four decimal places as needed.)
Interpret these answers in context.
For samples of 12 men, the possible sample mean| brain weights have a normal distribution with a mean of 1.1| kg and a standard deviation of |0.0346| kg.
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