In: Math
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.)
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 - 0.998565 ----- ( We look in to standard normal table across z value 2.9 and 0.08 )
= 0.001435