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