Question

Assume that people's weights can be described by a normal distribution with a mean of 68kg and a standard deviation of 9kg. If a small elevator has an operating limit of 430kg, what is the probability that the elevator will work with 6 people on board?

Answer 1

= 68 kg

= 9 kg

Number of people, n = 6

Sampling distribution of mean, will be approximately normal with mean,

= = 68 kg

=

=

= 3.67 kg

P(elevator will work) = P(total weight of 6 people is below 430 kg)

= P(mean weight of a sample of 6 will be less than 430/6)

= P( < 71.67)

= P(Z < (71.67 - 68)/3.67)

= P(Z < 1.00)

= 0.8413