For the following, use a normal distributionor a t-distribution to construct a 95% confidence interval for the populationmean. Justify your decision. If neither distribution can be used, explain why. Ifconvenient, use technology to construct the confidence interval. 25. Sports Cars: Miles per Gallon You take a random survey of 25 sportscars and record the miles per gallon for each. The data are listed below.Assume the miles per gallon are normally distributed.15 27 24 24 20 2124 14 2125 2113 21 25 22 21 25 2422 24 24 22 21 24 2426. ACT Scores In a recent year, the standard deviation of ACT scores forall students was 4.8. The ACT scores for 20 randomly selected studentsare listed below. Assume the test scores are normally distributed. (Source:ACT, Inc.)26 22 23 12 19 25 23 21 25 1017 26 23 24 20 14 21 23 20 2227. Hospital Waiting Times In a random sample of 19 patients at a hospital'sminor emergency department, the mean waiting time (in minutes) beforeseeing a medical professional was 23 minutes and the standard deviation was11 minutes. Assume the waiting times are not normally distributed.

25. Sports Cars: Miles per Gallon You take a random survey of 25 sports cars and record the miles per gallon for each. The data are listed below. Assume the miles per gallon are normally distributed. 15 27 24 24 20 21 24 14 21 25 21 13 21 25 22 21 25 24 22 24 24 22 21 24 24

25. Sports Cars: Miles per Gallon You take a random survey of 25 sports cars and record the miles per gallon for each. The data are listed below. Assume the miles per gallon are normally distributed. 15 27 24 24 20 21 24 14 21 25 21 13 21 25 22 21 25 24 22 24 24 22 21 24 24

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 26PFA

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Question

For the following, use a normal distribution or a t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. If convenient, use technology to construct the confidence interval.

25. Sports Cars: Miles per Gallon You take a random survey of 25 sports
cars and record the miles per gallon for each. The data are listed below.
Assume the miles per gallon are normally distributed.
15 27 24 24 20 21
24 14 21
25 21
13 21 25 22 21 25 24
22 24 24 22 21 24 24
26. ACT Scores In a recent year, the standard deviation of ACT scores for
all students was 4.8. The ACT scores for 20 randomly selected students
are listed below. Assume the test scores are normally distributed. (Source:
ACT, Inc.)
26 22 23 12 19 25 23 21 25 10
17 26 23 24 20 14 21 23 20 22
27. Hospital Waiting Times In a random sample of 19 patients at a hospital's
minor emergency department, the mean waiting time (in minutes) before
seeing a medical professional was 23 minutes and the standard deviation was
11 minutes. Assume the waiting times are not normally distributed.

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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