9 . (9 points) Men’s weights are normally distributed with mean 170 pounds and s

Question

9. (9 points)  Men’s weights are normally distributed with mean 170 pounds and standard deviation 20 pounds.

(a) Find the probability that a randomly selected man has a weight between 150and 200. (Show work and round the answer to 4 decimal places)

(b) What is the 75th percentile for men’s weight? (Show work and round the answer to 2 decimal places)

(c) If 64 men are randomly selected, find the probability that sample mean weightis greater than 175. (Show work and round the answer to 4 decimal places)

Explanation / Answer

using the standard variable Z for normal distribution we have

a)

P( 150-170 / 20 < z < 200-170 / 20 )

P( -1 < z < 1.5) = 1 - 0.1587 - 0.0668 = 0.7745

b)

P( z < z ) = 0.75 == P( z > z ) = 0.25

z = 0.67

0.67 = x-170 / 20

x=183.4

c)

P( x > 175)

P( z > 175-170 / 20/srqt64 )

P( z > 2 ) = 0.0228

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