Use the standard normal distribution or the t-distribution to construct a95%confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a random sample of45people, the mean body mass index (BMI) was26.7and the standard deviation was6.09. Question content area bottomPart 1Which distribution should be used to construct the confidence interval? Choose the correct answer below. A.Use a normal distribution because the sample is random,n≥30,andσis known. B.Use a t-distribution because the sample is random, the population is normal, andσis unknown. C.Use a t-distribution because the sample is random,n≥30,andσis unknown. D.Use a normal distribution because the sample is random, the population is normal, andσis known. E.Neither a normal distribution nor a t-distribution can be used because either the sample is not random, orn<30,and the population is not known to be normal.

Given, Sample mean(x̅) = 26.7 Standard deviation(s) = 6.09 Sample size (n) = 45 α = 1- 0.95 = 0.05…

Answered: Use the standard normal distribution or…

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 content area bottom

Part 1

Which distribution should be used to construct the confidence interval? Choose the correct answer below.

Use a normal distribution because the sample is random,

n≥30,

and

is known.

Use a t-distribution because the sample is random, the population is normal, and

is unknown.

Use a t-distribution because the sample is random,

n≥30,

and

is unknown.

Use a normal distribution because the sample is random, the population is normal, and

is known.

Neither a normal distribution nor a t-distribution can be used because either the sample is not random, or

n<30,

and the population is not known to be normal.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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