Question
In: Statistics and Probability
In June 2012, the average Amercian credit card account balance was US$3,127. Assuming that these balances...
In
June 2012, the average Amercian credit card account balance was
US$3,127.
Assuming that these balances are approximately normally
distributed with a mean of US$3,127 and a standard deviation of
US$1,500:
a) P(that an account balance is less than $2,500).
(Use diagram to show.)
b) one quarter of credit card accounts carry at least what
balance? (Use diagram to Show)
Solutions
Expert Solution
a)
The following is obtained graphically:
b)
We know that X is normally distributed, with parameters:
We need to find a score x so that the corresponding cumulative normal probability is equal to 0.25. Mathematically, x is such that:
The corresponding z score so that the cumulative standard normal probability distribution is 0.25 is
zc=-0.6745
This value of zc=-0.6745 can be found either with Excel, or with a normal distribution table. Hence, the X score associated with the 0.25 cumulative probability is
The following is obtained graphically:
Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!
orchestra answered 2 years agoRelated Solutions
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