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?

The formula we are given is z=x̄-μ/(σ/√n)

Answer 1

Solution:

Let $X$ be the random variable.

Given, $\mu=140 ; \sigma=25$

And an average weight for a sample of 11 would cause the total weight to exceed the 1650 pounds weight limit.

${\overline{x}}=\frac{1650}{11}=150$

We need to find $P(X>150)$.

Now, $z=\frac{{\overline{x}}-\mu}{\sigma}=\frac{150-140}{25}=0.4$

$P(Z>z)=P(Z>0.4)=0.3445 \approx 0.35$

Thus, required probability is 0.35.