QUESTION 8 Section 51 alimony income received by women is 40

QUESTION 8 (Section 5.1) alimony income received by women is $4,000. Assume a standard deviation of $7,500. Suppose 100 women a) Determine the probability that the mean annual allimony received by the 100 woman is within $500 of the necessary to assume that the population of annual alimony payments is normally distributed? Explain probability that the mean annual alimony recelved by the 1000 woman is within $500 of the incomes considered here, why is it necessary to take such a large sample in order to be According to the Current Population Reports, published by the U.S. Bureau of the census, the mean annual are selected at random. population mean (sentence). b) Is it c) Determine the your answer population mean (sentence. d) For the alimony assured of a relatively small sampling error?

Solution

mu = 4000 and sigma =7500

Sample size n =100

STd error = 7500/rt 100 = 750

X is normal (4000, 750)

a) P(|x-mu|<500) = P(|Z|<0.667)

= 0.4972

b) For sample size large, x bar follows normal irrespective of original distribution. Hence it can be assumed to follow normal.

c) When n =1000

std error = 7500/rt 1000 = 237.17

P(|x-mu}<500) = P(|z|<2.11)

=2(0.4826) = 0.9652

d) Because when n increases std error decreases thus giving a less margin of error and a narrow confidence interval.

This implies the relative small sampling error.