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 to 1610 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 than 161 lb.​ (Assume that weights of males are normally distributed with a mean of 165 Ib and a standard deviation of 35 lb). Does this elevator appear to be​ safe?

The probability the elevator is overloaded is:____.

Answer 1

The probability is "0.6406", this elevator isn't appear to be​ safe

Explanation:

The given values are:

Mean,

`\mu=165`

Standard deviation,

`\sigma=35`

Number of male passengers,

`n = 10`

Now,

⇒
`z=(161-165)/((\sigma)/(√(10) ) )`

`=(161-165)/((35)/(√(10) ) )`

hence,

The probability will be:

=
`P(\bar {x}>161)`

=
`P(z > -0.3614)`

=
`0.6406`