Question

an elevator has a placard stating that the maximum capacity is 3600 lb - 25 passengers. so, 25 adult male passengers can have a mean weight of up to 3600 / 25 = 144 pounds. assume that weights of males are normally distributed with a mean of 185 lb and a standard deviation of 27 lb.
a. find the probability that 1 randomly selected adult male has a weight greater than 144 lb.
b. find the probability that a sample of 25 randomly selected adult males has a mean weight greater than 144 lb.
c. what do you conclude about the safety of this elevator?
a. the probability that 1 randomly selected adult male has a weight greater than 144 lb is
(round to four decimal places as needed.)

Explanation:

Step1: Calculate the z - score for a single adult male

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 144\), \(\mu=185\), and \(\sigma = 27\).

$$z=\frac{144 - 185}{27}=\frac{-41}{27}\approx - 1.52$$

Step2: Find the probability using the standard normal distribution

We want \(P(X>144)\). Since \(P(X>144)=1 - P(X\leq144)\), and from the standard normal table, \(P(Z\leq - 1.52)=0.0643\)

$$P(X>144)=1 - 0.0643=0.9357$$

Answer:

\(0.9357\)