Hi, I\'m having trouble with this HW problem, Please provide answers and show wo

Question

Hi, I'm having trouble with this HW problem, Please provide answers and show work for problems a,b,c,d

The mean credit card debt for a 30 year old FEMALE living in NYC is approximately normally distributed with a mean debt of $8,478 and a standard deviation of $1,665. For parts a thru c, what is the probability that a 30 year old FEMALE living in NYC selected at random will have: a) A credit card debt less than $6,000? b) A credit card debt greater that $13,000? c) A credit card debt between $7,000 and $10,000? d) What minimum credit card debt that would separate the highest 5% credit card debt for a 30 year old female living in NYC?

Explanation / Answer

A)

since mean = 8478,s.d=1665,
The probability of less than 6000 is P ( X<6000)=

=P ( X<60008478 )

=P{(X)/<(6000-8478)/1665)

Since{ (X)/} =z

P(z<-1.49)

=0.683

B)

since mean = 8478,s.d=1665,
The probability of greater than 13000 is P ( X>13000)=

=P ( X>130008478 )

=P{(X)/>(13000-8478)/1665)

Since{ (X)/} =z

P(z<2.72)

=0.0033

C)
Since =8478 and =1665 we have:

P (7000<X<10000 )=P ( 70008478< X<10000-8478) )

P ( (70008478)/1665<(X)/<(10000-8478)/1665)

Since Z=(x)/ , (70008478)/1665= -0.88and (100008478 )/1665=0.92

we have:

P ( 7000<X<10000)=P ( 0.88<Z<0.92 )

Use the standard normal table to conclude that:

P ( -0.88<Z<0.92)=0.6323

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