# Z-Score Applications

An elevator has a design capacity of 2,560 pounds and a posted limit of 16 passengers. The weight of adults is approximately normal with a mean of 150 pounds and standard deviation of 20 pounds.

Find the probability that the elevator will be overloaded if 16 people are in the elevator. How many passengers would you recommend if you wanted to be sure that the overloading probability is less than 0.001?

I need a full explanation of this problem please! My teacher gave me this start, but I still don't understand.

Question 8 is asking you to find the probabiity that the total weight is greater than 2560 pounds. We know that the mean is 150 pounds with a suggested capacity of 15 people. The question asks about 16 people though (n=16). If you divide 2560 by 16= 160 pounds. This becomes your x. Then apply the formula for determining the z value.

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#### Solution Preview

An elevator has a design capacity of 2,560 pounds and a posted limit of 16 passengers. The weight of adults is approximately normal with a mean of 150 pounds and standard deviation of 20 pounds.

Find the probability that the elevator will be overloaded if 16 people are in the elevator. How many passengers would you recommend if you wanted to be sure that the overloading probability is less than 0.001?

(1) Find the probability that the elevator will be overloaded if 16 people are in the elevator.

If 16 people are in the elevator, the elevator will be overloaded if the average weight of those 16 people is more than 160 lbs ...