Answer to Question #209987 in Statistics and Probability for nena

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 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

a. The sum of normal distributions is a normal distribution with mean as the sum of means and variance as the sum of variances. Thus,

$\mu =15\times76=1140$

$\sigma^2=15\times 90.25=1353.75$

$\sigma=\sqrt{1353.75}=36.79$

The weight of the 15 passengers is normally distributed with mean 1140 and standard deviation of 36.79.

b.

$P(x>1200)$

$=P(z>\frac{1200-1140}{36.79})$

$=P(z>1.631)$

$=0.0515$

The probability that the lift will be overloaded is 0.0515 which is low. Thus, it is not likely that the lift will be overloaded.