The capacity of an elevator is 1010 people or 16001600 pounds. The capacity will

Question

The capacity of an elevator is 1010 people or 16001600 pounds. The capacity will be exceeded if 1010 people have weights with a mean greater than 1600 divided by 10 equals 160 pounds.1600/10=160 pounds. Suppose the people have weights that are normally distributed with a mean of 164 lb164 lb and a standard deviation of 29 lb29 lb. a. Find the probability that if a person is randomly selected, his weight will be greater than 160160 pounds. The probability is approximately nothing. (Round to four decimal places as needed.) b. Find the probability that 1010 randomly selected people will have a mean that is greater than 160160 pounds. The probability is approximately nothing. (Round to four decimal places as needed.) c. Does the elevator appear to have the correct weight limit? Why or why not? A. Yes, there is a good chance that 1010 randomly selected people will not exceed the elevator capacity. B. No, 1010 randomly selected people will never be under the weight limit. C. Yes, 1010 randomly selected people will always be under the weight limit. D. No, there is a good chance that 1010 randomly selected people will exceed the elevator capacity. Click to select your answer(s).

Explanation / Answer

a) probability that if a person is randomly selected, his weight will be greater than 160 pounds

=P(X>160) =1-P(X<160)=1-P(Z<(160-164)/29)=1-P(Z<-0.1379)=1-0.4451 =0.5549

b)

here std errror of mean =std deviation/(n)1/2 =29/(10)1/2 =9.1706

probability that 10 randomly selected people will have a mean that is greater than 160 pounds

=P(X>160) =1-P(X<160)=1-P(Z<(160-164)/9.1706)=1-P(Z<-0.4362)=1-0.3314 =0.6686

c)

option D is correct

D. No, there is a good chance that 10 randomly selected people will exceed the elevator capacity.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.