he overhead reach distances of adult females are normally distributed with a mean of 202.5 cm and a standard deviation of 8 cm. a. Find the probability that an individual distance is greater than 215.00 cm. b. Find the probability that the mean for 15 randomly selected distances is greater than 200.30 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

he overhead reach distances of adult females are normally distributed with a mean of 202.5 cm and a standard deviation of 8 cm. a. Find the probability that an individual distance is greater than 215.00 cm. b. Find the probability that the mean for 15 randomly selected distances is greater than 200.30 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

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

The overhead reach distances of adult females are normally distributed with a mean of

202.5 cm

and a standard deviation of

8 cm.

a. Find the probability that an individual distance is greater than

215.00

cm.

b. Find the probability that the mean for

randomly selected distances is greater than 200.30 cm.

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

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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