In: Statistics and Probability
Weights of men are normally distributed with a mean of 189 lb and a standard deviation of 39 lb. If 14 men are randomly selected, find the probability that they have weights with a mean greater than 174 lb.
Solution :
Given that,
mean = = 189
standard deviation = = 39
n = 14
=189
= / n = 39 14 = 10.4232
P ( > 174 )
= 1 - P ( < 174 )
= 1 - P ( - /) < ( 174 - 189 / 10.4232)
= 1 - P ( z <- 15 / 10.4232 )
= 1 - P ( z < -1.44)
Using z table
= 1 - 0.0749
=0.9251
Probability = 0.9251