Weights of men are normally distributed with a mean of 180 pounds and a standard deviation...

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?

Solutions

Expert Solution

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

orchestra answered 1 year ago

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