In Exercises 23-28, use a normal distributionor a t-distribution to construct a 95% confidence interval for the populationmean. Justifv vour decision. If neither distribution can be used, explain why. Ifconvenient, use technology to construct the confidence interval 23. Lengths of Bolts In a random sample of 70 bolts, the mean length was1.25 inches and the standard deviation was 0.05 inch.24. Prices of Toasters You took a random sample of 12 two-slice toasters andfound the mean price was $57.79 and the standard deviation was $19.05.Assume the prices are normally distributed.| 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 21 24 14 2125 21 13 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.28. Solo Tent Costs In a random sample of 18 one-person tents, the mean pricewas $144.19 and the standard deviation was $61.32. Assume the prices arenormally distributed.

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23. Lengths of Bolts In a random sample of 70 bolts, the mean length was 1.25 inches and the standard deviation was 0.05 inch.

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

100%

In Exercises 23-28, use a normal distribution or a t-distribution to construct a 95% confidence interval for the population mean. Justifv vour decision. If neither distribution can be used, explain why. If convenient, use technology to construct the confidence interval

23. Lengths of Bolts In a random sample of 70 bolts, the mean length was
1.25 inches and the standard deviation was 0.05 inch.
24. Prices of Toasters You took a random sample of 12 two-slice toasters and
found the mean price was $57.79 and the standard deviation was $19.05.
Assume the prices are 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
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.
28. Solo Tent Costs In a random sample of 18 one-person tents, the mean price
was $144.19 and the standard deviation was $61.32. Assume the prices are
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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