the standard deviation of the distribution of sample means This Question: 1 pt 4

Question

the standard deviation of the distribution of sample means This Question: 1 pt 4 of 11 (3 This Quiz: 11 pts possibie Question Help * The capaty of an elevator is 8 people or 1208 pounds The capacity wil be exceeded #8 people have weights with a mean greater than 1208/8e 151 pounds. Suppose the people have weights that are normally distributed with a mean of 160 lb and a standard deviation of 27 lb selected The probabilty is approximately . (Round to four dec mal places as needed.) The probabil ty is approximately (Round to four ernal places as needed ) of 4 c. Does the elevator appear to have the correct weight limit? Why or why not? O A. Yes, there is a good chance that 8 randomly selected people vill not exceed the elevator capacty O C. Yes, 8 randomly selected people will always be under the weight im ontelB. No, 8 randomly selected people will never be under the weight limit O D. No, there is a good chance that 8 randomly selected people will ex.ceed the elevator or 4 dia L se O on Tutor

Explanation / Answer

Answer to the question is as follows:

a.

P(X>151)

= P(Z> 151-160 / 27)

= .3707

b.

P(X>151)

= P(Z> 151-160 / (27/sqrt(8))

= .4536

c.

B is wrong as P(X>1510 is not very small. But still the ratio is less than .5, which means that there is less than a fair chance of elevator taking up the capacity of 8 people. Hence, answer is a D is right.

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