Heights of 10-year-old boys (5th graders) follow an approximate normal distribution with mean of 55.5 inches and standard deviation of 2.7 inches. a. What proportion of 10-year-old boys are between 4 ft 4 in and 5 ft (between 52 inches and 60 inches) tall? (Include an appropriate picture, calculator/stat key documentation, and box your final answer, including units.) b. A researcher takes many random samples of size n = 400 and calculates the mean of the samples, X. Create the sampling distribution for this sampling mean . What is the center and standard error of this new sampling distribution? Draw and label the distribution and provide at least five points on the horizontal axis. Standard Error: _ Center: c. Consider the distribution of sample means in part b. What is the cut-off value for a sample mean where only 20% of the sample means will be lower? (Include an appropriate picture and provide calculator/stat key documentation.) d. What famous principle from statistics allows you to assume the shape, center, and spread of the distribution in b.
Heights of 10-year-old boys (5th graders) follow an approximate normal distribution with mean of 55.5 inches and standard deviation of 2.7 inches. a. What proportion of 10-year-old boys are between 4 ft 4 in and 5 ft (between 52 inches and 60 inches) tall? (Include an appropriate picture, calculator/stat key documentation, and box your final answer, including units.) b. A researcher takes many random samples of size n = 400 and calculates the mean of the samples, X. Create the sampling distribution for this sampling mean . What is the center and standard error of this new sampling distribution? Draw and label the distribution and provide at least five points on the horizontal axis. Standard Error: _ Center: c. Consider the distribution of sample means in part b. What is the cut-off value for a sample mean where only 20% of the sample means will be lower? (Include an appropriate picture and provide calculator/stat key documentation.) d. What famous principle from statistics allows you to assume the shape, center, and spread of the distribution in b.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 1GP
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Transcribed Image Text:Heights of 10-year-old boys (5th graders) follow an approximate normal distribution with mean of 55.5 inches and
standard deviation of 2.7 inches.
a. What proportion of 10-year-old boys are between 4 ft 4 in and 5 ft (between 52 inches and 60 inches) tall?
(Include an appropriate picture, calculator/stat key documentation, and box your final answer, including units.)
b. A researcher takes many random samples of size n = 400 and calculates the mean of the samples, . Create the
sampling distribution for this sampling mean . What is the center and standard error of this new sampling
distribution? Draw and label the distribution and provide at least five points on the horizontal axis.
Standard Error:
Center:
c. Consider the distribution of sample means in part b. What is the cut-off value for a sample mean where only 20% of
the sample means will be lower? (Include an appropriate picture and provide calculator/stat key documentation.)
d. What famous principle from statistics allows you to assume the shape, center, and spread of the distribution
in b.
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