A particular credit card company has noted that one population of new customers

Question

A particular credit card company has noted that one population of new customers has tIansferred balances from other credit cards. The average transfer balance has been $1000 with a standard deviation of $250. The distribution of transfer balances has been normal. (a) What is the probability that the transfer balance was less than $100? (b) Wha is quartile one and quartile three for transfer balances? Interpret. (c) What is the median transfer balance? (d) The credit card company has noticed that whenever the transfer balance is at least $400, it takes the new customer at least two months to pay off the balance. What is the probability of this event? (e) The credit card company has also noticed that whenever the transfer balance is at least $1400, it takes the customer at least 6 months to pay off the balance. What is the probability of this outcome?

Explanation / Answer

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We have been given the params of the normal distribution:

Average = 1000
Stdev = 250

a. P(X<100) = P(Z< 100-1000/250) = 0.000159109

b. Q1 is basically the 25 percentile 'or'
P(X<c) = .25
We have a Z value -0.675
Therefore,
P(Z< c-1000 / 250) = .25
(c-1000)/250 = -.675
c = -0.675*250 + 1000 = $831.25
The 25th percentile is $831.25

Q3 is basically the 75th percentile
P(X<c) = .75
We have the Z value as +0.675
Therefore,
P(Z< c-1000 / 250) = .75
(c-1000)/250 = .675
c = 0.675*250 + 1000 = $1168.75
The 75th percentile is $1168.75

c. The median transfer is basically the value at 50th percentile

or for Z=0, therefore,
P(X<c) = .5
(C-1000)/250 = 0
c = 1000
So, the median is at $1000

d. P(X>400) =P(Z> 400-1000/ 250) = P(Z>-2.4)= .9918

e. P(X>1400) = P(Z> 1400-1000/250) = .055

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