Question

An elevator has a placard stating that the maximum capacity is 1610 lb---10 passengers.​ So, 10 adult male passengers can have a mean weight of up to1610 divided by 10 = 161 pounds. If the elevator is loaded with 10 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than161lb.​ (Assume that weights of males are normally distributed with a mean of 165 lb and a standard deviation of 35 lb.)Does this elevator appear to be​ safe?The probability the elevator is overloaded is?​(Round to four decimal places as​ needed.)

Answer 1

Answer:

$\mu = 165$

$\sigma = 35$

We are supposed to find  the probability that it is overloaded because they have a mean weight greater than 161 lb.

n = 10 males

P(X>161)

Formula : $z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

$z=\frac{161-165}{\frac{35}{\sqrt{10}}}$

$z=-0.3614$

Refer the z table

P(z<−0.3614)=0.6406

P(x>161)=1-P(x<161)=1-P(z<−0.3614)=1-0.6406=0.3594

The probability the elevator is overloaded is 0.3594

The elevator is safe since the probability of overload is less than 0.5