Answer:
Explained below.
Step-by-step explanation:
According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.
Then, the mean of the sample means is given by,
And the standard deviation of the sample means is given by,
a
The expected value of the sample mean of their weights is same as the population mean, <em>μ</em> = 1515 lbs.
b
The standard deviation of the sampling distribution of the sample mean weight is:
c.
The average weights for a sample of 16 people will result in the total weight exceeding the weight limit of 2500 lbs. is:
d
Compute the probability that a random sample of 16 persons on the elevator will exceed the weight limit as follows: