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 178 lb and a standard deviation of 37 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 (square).
(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 \(x = 144\), \(\mu=178\), and \(\sigma = 37\).

$$z=\frac{144 - 178}{37}=\frac{- 34}{37}\approx - 0.92$$

Step2: Find the probability using the standard normal distribution

We want \(P(X>144)\). Since \(P(X>x)=1 - P(X\leq x)\), and for \(z=-0.92\), from the standard - normal table \(P(Z\leq - 0.92)=0.1788\)

$$P(X > 144)=1-0.1788 = 0.8212$$

Answer:

\(0.8212\)