Problem

1

(Please use

the

z

-

Table.)

The ABC Bank estimates that the annual credit card balance

of their customers

is normally

distributed with mean $5000 and standard deviation

of $1500.

(a)

What is the probability that the

annual credit card balance

of a single randomly selected

customer of ABC Bank exceeds $8000?

(b) Ten percent of the customers of this bank will have an annual credit balance of at least how

many

dollars?

(c) What is the probability that 25 randomly sampled customers will have a sample mean

credit

card balance

between

$4000 and $6000

?

(

d

) What should the cut

-

off

L

be if the ABC Bank wants at least a 10% chance that the average

cred

it card balance

of a sample of 25 randomly selected customers falls above

L

?