Answer to Question #173685 in Statistics and Probability for Janina

Question

An elevator in the hospital has a weight limit of 1650 pounds. Suppose an average weight of

the people who use this elevator is 140 pounds with a standard deviation of 25 pounds.

Assuming that the distribution of weights is approximately normal and a random sample of

11 people are selected, what is the probability that the random sample will exceed the weight

limit?

Answer 1

$X;\mu=140;\sigma=25$

$\text{an average weight for a sample of 11 would cause the}\newline \text{ total weight to exceed the 1650 lb weight limit}$

$\bar{x_{lim}}=\frac{1650}{11}=150$

$P(X>150)$

$z= \frac{150-\mu}{\sigma}=0.4$

$P(Z>z)=P(Z>0.4)= 0.3445\approx0.35$

Answer: 0.35 probability that a random sample of 11 people will exceed the weight limit