Question

On the distant planet Cowabunga, the weights of cows have a normal distribution with a mean of 400 pounds and a standard deviation of 43 pounds. The cow transport truck holds 12 cows and can hold a maximum weight of 5076.

If 12 cows are randomly selected from the very large herd to go on the truck, what is the probability their total weight will be over the maximum allowed of 5076? (This is the same as asking what is the probability that their mean weight is over 423.)

Answer 1

Solution :

Given that ,

mean = = 400

standard deviation = = 43

n = 12

= 400

(a) = / n = 43 / 12 = 12.4130

P( >5076 ) = 1 - P( < 5076)

= 1 - P[( - ) / < (5076 - 400) / 12.4130]

= 1 - P(z <376.70 )

Using z table,    

= 1 - 1

= 0

(b )P( >423 ) = 1 - P( < 123)

= 1 - P[( - ) / < (423 - 400) / 12.4130]

= 1 - P(z <1.85 )

Using z table,    

= 1 - 0.9678

= 0.0322