The capacity of an elevator is 12 people or 1836 pounds. The capacity will be ex

Question

The capacity of an elevator is 12 people or 1836 pounds. The capacity will be exceeded if 12 people have weights with a mean greater than 1836 / 12 = 1 Suppose the people have weights that are normally distributed with a mean of 160 lb and a standard deviation of 28 lb. Find the probability that if a person is randomly selected, his weight will be greater than 153 pounds. The probability is approximately .5987 . (Round to four decimal places as needed.) Find the probability that 12 randomly selected people will have a mean that is greater than 153 pounds. The probability is approximately (Round to four decimal places as needed.) Enter your answer in the answer box and then click Check Answer.

Explanation / Answer

Let X be the random variable that Peoples height.

Given that X ~ Normal (mean = 160, sd = 28)

Find the probability that if a person is randomly selected his weight will be greator than 153 pounds.

We have to find P(X > 153).

Convert x=153 into z-score.

z = (x - mean) / sd = (153 - 160) / 28 = -0.25

That is now we have to find P(Z > -0.25).

We can find this probability by using EXCEL.

syntax :

=1 - NORMSDIST(z) (EXCEL always gives left tailed probability)

where z is test statistic value.

P(Z > -0.25) = 0.5987

Find the probability that 12 randomly selected people will have a mean that is greator than 153 pounds.

n = 12

So here we have to find P(Xbar > 153).

But we know that Xbar ~ Normal (mean = 160, sd = 28/sqrt(12) )

Xbar has mean is 160 and standard deviation is 8.0829.

Convert Xbar into z-score.

z = (153 - 160) / 8.0829 = -0.8660

That is now we have to find P(Z > -0.87).

P(Z > -0.87) =0.8068

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