Elements of Statistics Section 7.3 1) The times of the finishers in the New York

Question

Elements of Statistics Section 7.3 1) The times of the finishers in the New York City 10km run are normally distributed with a mean of 61 minutes and a standard deviation of 9 minutes. A) Find the mean and the standard error of the sample mean for samples of size 4 B) Repeat part (A) for samples of size 9 C) Obtain the percentage of all samples of four finishers that have mean finishing times within 5 minutes of the population mean finishing time of 61 minutes. Loan amounts of loans originated by a large insurance-company lender have a mean of $6.74 million with a standard deviation of $15.37 million. The variable "loan amount" is known to have a right-skewed distribution. a) Determine the mean and the sampling error of the sample mean for samples of size 200. 2) b) Repeat part (a) for samples of size 600. Why can you still answer parts (a) and (b) when the distribution of loan amounts is not normal, but rather right skewed ? c) What is the probability thtat the sampling error made in estimating the population mean loan amount by the mean loan amount of a simple random sample of 200 loans will be at most $1 million ? d) e) Repeat part (d) for samples of size 600.

Explanation / Answer

1)

a)
mean (Xbar) = E(X) = 61
standard error = sd(X) /sqrt(n) = 9 /sqrt(4) = 9/2 = 4.5

b)
when n = 9
mean remains same
standard error = 9/sqrt(9) = 9/3 = 3

c)
we need
P(|Xbar - mean| < 5)
= P(|Z| < 5 /4.5)    Z = (Xbar - mean)/standard error
= P(|Z| < 10/9)
=0.7335

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