Question

Z=

x-μ
σ
Z=
x-μ
°/√n
d
σ
orotal =
Standard Deviation=
√no
Otis Elevators conducted a study and determined the mean weight for American
adults is 180 lb with a standard deviation of30lb. The distribution is approximately
normally distributed.
(a) What is the probability of a randomly selected adult weighing more than 225
pounds?
Answer=
(enter a number between 0 and 1, 4 decimal places)
A random sample of 16 American adults is taken.
(b) What is the mean and standard deviation of the sample means?
Mean=
lb
lb (1 decimal place
Otis Elevators is installing an elevator in a large office building that will have a capacity
of 16 people and a maximum load of 3,600 pounds.
(c) If there are 16 people in the elevator, that maximum load will be exceeded if the
mean weight of the 16 people is above what weight?
Answer=
lb
(d) Approximately, what is the probability that load will be exceeded if there are
16 people in the elevator?

Answer 1

Answer: (a) Using the Z-score formula, we have:

Z = (225 - 180) / 30 = 1.5

Using a standard normal distribution table, we find that the probability of a randomly selected adult weighing more than 225 pounds is approximately 0.0668.

(b) The mean of the sample means is equal to the population mean, which is 180 pounds. The standard deviation of the sample means is given by:

σ/√n = 30/√16 = 7.5 pounds

(c) The total weight of the 16 people in the elevator should not exceed the maximum load of 3,600 pounds. Therefore, the mean weight of the 16 people should not exceed:

3,600 / 16 = 225 pounds

(d) Using the central limit theorem, we can approximate the distribution of the sample means to be approximately normal with a mean of 180 pounds and a standard deviation of 7.5 pounds. To find the probability that the load will be exceeded, we can find the probability that the sample mean is greater than 225 pounds. Using the Z-score formula:

Z = (225 - 180) / 7.5 = 6

Since the Z-score is extremely high, the probability of the sample mean being greater than 225 pounds is extremely low and can be approximated as 0.

Explanation: