Question

An elevator has a weight capacity of 3000 lbs. Sixteen men get into the elevator. Given the weights of men are normally distributed with a mean of 172 lbs and a std dev of 29 lbs find the probability of these men exceeding the maximum weight, thus breaking the cable and plunging to their death. _________

Answer 1

X : weights of men

X follows normal distribution with mean 172 lbs and a std dev of 29 lbs

16 Men get into the elevator: 16X

Y = 16X is also a normal distribution with mean :16 x 172 and std dev of 16 x 29 lbs

Mean = 2752

standard deviation = 464

i.e Y follows normal distribution with mean = 2752 and standard deviation = 464

Elevator Maximum weight capacity = 3000lbs

probability of these men exceeding the maximum weight = P(Y > 3000)

P(Y > 3000) = 1- P(Y3000)

P(Y3000)

Z-score for 3000 = (3000 - 2752)/464 = 248/464 = 0.53

From standard normal tables,

P(Z<0.53) = 0.7019

P(Y3000) = P(Z<0.53) = 0.7019

P(Y > 3000) = 1- P(Y3000) = 1-0.7019 = 0.2981

Probability of these men exceeding the maximum weight, thus breaking the cable and plunging to their death = 0.2981