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

Answer:

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

Step-by-step explanation:

The given values are:

Mean,

$\mu=165$

Standard deviation,

$\sigma=35$

Number of male passengers,

$n = 10$

Now,

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

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

hence,

The probability will be:

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

= $P(z > -0.3614)$

= $0.6406$