The overhead reach distances of adult females are normally distributed with a mean of 197.5 cm and a standard deviation of 8.3 cm. a. Find the probability that an individual distance is greater than 206.80 cm. b. Find the probability

The overhead reach distances of adult females are normally distributed with a mean of 197.5 cm and a standard deviation of 8.3 cm. a. Find the probability that an individual distance is greater than 206.80 cm. b. Find the probability

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

Section13.3: Special Probability Density Functions

Problem 8E

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Question

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

197.5 cm

and a standard deviation of

8.3 cm.

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

206.80

cm.

b. Find the probability that the mean for

randomly selected distances is greater than 195.70 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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