A local bank has determined that the daily balances of the checking accounts of
ID: 375215 • Letter: A
Question
A local bank has determined that the daily balances of the checking accounts of its customers are normally distributed with an average of $280 and a standard deviation of $20.
a.
What percentage of its customers has daily balances of more than $275?
b.
What percentage of its customers has daily balances less than $243?
c.
What percentage of its customers' balances is between $241 and $301.60?
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a.
What percentage of its customers has daily balances of more than $275?
b.
What percentage of its customers has daily balances less than $243?
c.
What percentage of its customers' balances is between $241 and $301.60?
Explanation / Answer
A.
Mean = $280
Standard deviation (SD) = $20
For customers has daily balances of more than $275
Z = (mean - 275)/SD = (280-275)/20 = .25
At this value of Z = .25, area covered = .5987 (as per the normal distribution table)
Hence, 59.87% people have daily balance of more than 275.
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B.
Mean = $280
Standard deviation (SD) = $20
For customers has daily balances less than $243
Z = (mean - 275)/SD = (280-243)/20 = 1.85
At this value of Z = 1.85, area covered = .9678 (as per the normal distribution table)
Hence, % of people with daily balance of less than $243 = 1-.9678 = .0322
So, 3.22% people have daily balance of less than the $243.
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C.
Mean = $280
Standard deviation (SD) = $20
For the case of percentage of its customers' balances is between $241 and $301.60
In Step 1, will be to know the people between $ 241 and 280,
Z = (280-241)/20 = 1.95
At the value of Z = 1.95, Area covered = .9744
Then,
Z = (280-301.6)/20 = -1.08
At Z = -1.08, the area covered = .1401
In step 2,
The % of people between $241 and $301.60 = .9744 - .1401 = .8343
So, the % of people with daily balance between $241 and $301.6 is 83.43%.
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