In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 69.5 inches and a standard deviation of 2.0 inches. A study participant is randomly selected. (a) Find the probability that a study participant has a height that is less than 65 inches.The probability that the study participant selected at random is less than 65 inches tall is(Round to four decimal places as needed.)(b) Find the probability that a study participant has a height that is between 65 and 71 inches.The probability that the study participant selected at random is between 65 and 71 inches tall is(Round to four decimal places as needed.)(c) Find the probability that a study participant has a height that is more than 71 inches.The probability that the study participant selected at random is more than 71 inches tall is(Round to four decimal places as needed.)(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.A. The event in part (b) is unusual because its probability is less than 0.05.B. The events in parts (b) and (c) are unusual because its probabilities are less than 0.05.O C. None of the events are unusual because all the probabilities are greater than 0.05.D. The event in part (a) is unusual because its probability is less than 0.05.

If X denotes the height of men, then, X ~N(69.5, 4.0) Thus, mean = u = 69.5 and SD = s = 2.0.

Answered: (a) Find the probability that a study…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 47E

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In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 69.5 inches and a standard deviation of 2.0 inches. A study participant is randomly selected.

(a) Find the probability that a study participant has a height that is less than 65 inches.
The probability that the study participant selected at random is less than 65 inches tall is
(Round to four decimal places as needed.)
(b) Find the probability that a study participant has a height that is between 65 and 71 inches.
The probability that the study participant selected at random is between 65 and 71 inches tall is
(Round to four decimal places as needed.)
(c) Find the probability that a study participant has a height that is more than 71 inches.
The probability that the study participant selected at random is more than 71 inches tall is
(Round to four decimal places as needed.)
(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.
A. The event in part (b) is unusual because its probability is less than 0.05.
B. The events in parts (b) and (c) are unusual because its probabilities are less than 0.05.
O C. None of the events are unusual because all the probabilities are greater than 0.05.
D. The event in part (a) is unusual because its probability is less than 0.05.

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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