Question

An elevator has a placard stating that the maximum capacity is

1240 lb —88 passengers.​ So,

88 adult male passengers can have a mean weight of up to

1240 divided by 8 equals 155 pounds.1240/8=155 pounds.

If the elevator is loaded with

88

adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than

155

lb.​ (Assume that weights of males are normally distributed with a mean of

164 lb164 lb

and a standard deviation of

26 lb26 lb​.)

Does this elevator appear to be​ safe?

The probability the elevator is overloaded is

nothing.

​(Round to four decimal places as​ needed.)

Answer 1

Solution :

Given that ,

= 164

= / n = 26 / 8 = 9.19

P( > 155) = 1 - P( < 155)

= 1 - P[( - ) / < (155 - 164) / 9.19]

= 1 - P(z < -0.98)   

= 1 - 0.1635

= 0.8365

No, there is a good chance that 8 randomly selected people will exceed the elevator capacity.