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a. For random samples of size n = 10, calculate the area under the sampling distribution curve for between the values μ-1 and μ + 1. That is, find the probability that the sample mean lies within ±1 unit of the population mean. b. Repeat the probability calculation in part (a) for samples of size n = 50, n = 100, and n = 1000. c. Graph the probabilities you found in parts (a) and (b) versus their corresponding sample sizes, n. What can you conclude from this graph?

a. For random samples of size n = 10, calculate the area under the sampling distribution curve for between the values μ-1 and μ + 1. That is, find the probability that the sample mean lies within ±1 unit of the population mean. b. Repeat the probability calculation in part (a) for samples of size n = 50, n = 100, and n = 1000. c. Graph the probabilities you found in parts (a) and (b) versus their corresponding sample sizes, n. What can you conclude from this graph?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 9CR
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 Random samples of size n are taken from a normal population whose standard deviation is known to be 5.  Answer the following attached parts of this question:

a. For random samples of size n = 10, calculate the area under the sampling distribution curve for between the values μ-1 and μ + 1. That is, find the probability that the sample mean lies within ±1 unit of the population mean. b. Repeat the probability calculation in part (a) for samples of size n = 50, n = 100, and n = 1000. c. Graph the probabilities you found in parts (a) and (b) versus their corresponding sample sizes, n. What can you conclude from this graph?
Transcribed Image Text:a. For random samples of size n = 10, calculate the area under the sampling distribution curve for between the values μ-1 and μ + 1. That is, find the probability that the sample mean lies within ±1 unit of the population mean. b. Repeat the probability calculation in part (a) for samples of size n = 50, n = 100, and n = 1000. c. Graph the probabilities you found in parts (a) and (b) versus their corresponding sample sizes, n. What can you conclude from this graph?
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