Answer to Question #210187 in Statistics and Probability for bareera

Question

There is a notice in a lift saying that the maximum weight allowed is 1200 kg.The weights of passengers are normally distributed with mean of 76 kg and a standard deviation of 9.5 kg 15 passenger get into the lift. (a) Calculate the mean and standard deviation of the total weights of 15 passengers.

Answer 1

$\mu=76,\sigma=9.5$

Maximum weight allowed=1200 kg

(a) n=15,

Sample mean $\bar{x}=\mu=76kg$

Sample standard deviation $s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{9.5}{\sqrt{15}}=2.452 kg$