In: Statistics and Probability
Weights of men are normally distributed with a mean of 180 pounds and a standard deviation of 25 pounds. A boat in Michigan will sink if the average weight of its 20 passengers is over 200 pounds. What is the probability that a group of 20 men will have an average weight greater than 200 pounds?
Solution :
Given that,
mean = = 180
standard deviation = =25
n=20
= =180
= / n =25 / 20= 5.5902
P( >200 ) = 1 - P( < 200)
= 1 - P[( - ) / < (200 -180) / 5.5902]
= 1 - P(z <3.58 )
Using z table
= 1 - 0.9998
= 0.0002
probability= 0.0002