Question

Men’s weights are normally distributed with mean 175 pounds and standard deviation 25 pounds.

(a) Find the probability that a randomly selected man has a weight between 140 and 190. (Show work and round the answer to 4 decimal places)

(b) What is the 80^th 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 weight is greater than 180. (Show work and round the answer to 4 decimal places)

Answer 1

Solution :

Given that ,

mean = = 175

standard deviation = = 25

a) P(140 < x < 190) = P[(140 - 175)/ 25) < (x - ) /  < (190 - 175) / 25) ]

= P(-1.40 < z < 0.60)

= P(z < 0.60) - P(z < -1.40)

Using z table,

= 0.7257 - 0.0808

= 0.6449

b) Using standard normal table,

P(Z < z) = 80%

= P(Z < z ) = 0.80

= P(Z < 0.8416 ) = 0.80

z = 0.8416

Using z-score formula,

x = z * +

x = 0.8416 * 25 + 175

x = 196.04

c) = 175

= / n = 25 / 64 = 3.125

P( > 180) = 1 - P( < 180)

= 1 - P[( - ) / < (180 - 175) / 3.125 ]

= 1 - P(z < 1.60)   

= 1 - 0.9452

= 0.0548