Question

Problem 2 (20pts) The mean balance that college students owe on their credit card is $1096 with a standard deviation of $350. If all possible random samples of size 144 are taken from this population, determine the following: a) name of the Sampling Distribution b) mean and standard error of the sampling distribution of the mean (use the correct name and symbol for each) c) percent of sample means for a sample of 144 college students that is greater than $1200 d) probability that sample means for samples of size 144 fall between $900 and $1200. e) Below which sample mean can we expect to find the lowest 25% of all the sample means?

Answer 1

ANSWER:

solution: - Given Dola Mean (1) =32096 Standard Deviation (6) -$350 Sample size (~) - 144 (a) Given that? Sampling Desfsibuljon o's -> Normal distribulion. is a Sompling defcbuhan (from Central limit therem since the sample Sige is large enough? (6) Given that: mean and standard Stands of sampling. Distilfun + mean of sampling distotleblon, I . 1096. slandard 3418 4 sampling disturile from & meam is an on s 350 . 350 EX .291167

104 (c) The degwed probabodily is => PC271200-1096) 29.167 * P(Z > Honden) = P(Z >3.566) from "2' table is. -0.0002 -0.02.1. (d) The requised probability is pl 900-1096 Jozs (1200-1096) . 29+167 29.167 op location <a ) P(-6172 <33.566 ) (0.49919+0149212 (-cabello) 20.9996 te) Given that Lower 25*1.the sample means. so 25%. Sample rean, the costi Cal Valee 2' is -0.6745 Requised mean a $1096 - 006745*829.162 a $ 1096 -19.673 - $10760327