1 The credit card debt of college seniors follows a normal d

1. The credit card debt of college seniors follows a normal distribution with mean $3,262 and standard deviation $1100. Show your work or calculator commands to answer the following questions.

A) What percent of college seniors owe less than $2000 to credit card companies? ____________________________________

B) Ninety percent of college seniors owe less than what amount of debt to credit card companies? ____________________________________

C) What is the probability that a randomly selected college senior owes more than $4200 to credit card companies? ____________________________________

D) For a random sample of 25 college seniors, what is the probability that their sample mean credit card debt is more than $4200? ____________________________________

E) Determine if any of the probabilities you found in parts C) and D) is an unusual probability. Justify your answer. _____________________________________

Solution

Mean ( u ) =3262
Standard Deviation ( sd )=1110
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X < 2000) = (2000-3262)/1110
= -1262/1110= -1.1369
= P ( Z <-1.1369) From Standard Normal Table
= 0.1278                  
b)
P ( Z < x ) = 0.9
Value of z to the cumulative probability of 0.9 from normal table is 1.282
P( x-u/s.d < x - 3262/1110 ) = 0.9
That is, ( x - 3262/1110 ) = 1.28
--> x = 1.28 * 1110 + 3262 = 4685.02                  
c)
P(X > 4200) = (4200-3262)/1110
= 938/1110 = 0.845
= P ( Z >0.845) From Standard Normal Table
= 0.199                  
d)
P(X > 4200) = (4200-3262)/1110/ Sqrt ( 25 )
= 938/222= 4.2252
= P ( Z >4.2252) From Standard Normal Table
= 0