Question

The weights of individuals who seek a helicopter ride in an amusement park have a mean of 180 lb and a standard deviation of 15 lb. The helicopter can carry five persons but has a maximum weight capacity of 1000 lb. What is the probability that the helicopter will not take off with five persons aboard? (Hint. Apply the central limit theorem.)

Answer 1

The helicopter can carry five persons but has a maximum weight capacity of 1000 lb. i.e maximum mean weight is 1000/5 =200.

Here we have = 180 , = 15 , n = 5

The helicopter will not take off with five persons abroad if maximum capacity exceeds 200 lb.

Hence the probability is given by

= p ( z > 2.981424 )

= 1 - p ( z 2.981424 )

= 1 - 0.998565 ----- ( We look in to standard normal table across z value 2.9 and 0.08 )

= 0.001435