Answer to Question #209997 in Statistics and Probability for Hakeema

Question

here is a notice in a lift saying that the maximum weight allowed is 1200 kg. The weights of passengers are normally distributed with a mean of 76 kg and a standard deviation of 9.5 kg. 15 passengers get into the lift. a. Calculate the mean and standard deviation of the total weight of 15 passengers. b. Is it likely that the lift will be overloaded with 15 passengers? Show some calculations to support your answer 

Answer 1

Solution:

Given, $\mu=76,\sigma=9.5,n=15$

(a):

Mean and standard deviation of sample:

$\mu_{\bar X}=76,\sigma_{\bar X}=\dfrac{\sigma}{\sqrt n}=\dfrac{9.5}{\sqrt{15}}=2.452$

(b):

Sum of weights of 15 passengers = 15 x 76 = 1140 kg,

which is less than 1200 kg (max. weight allowed).

Hence, it is not likely that the lift will be overloaded.