Question

 

The Webster National Bank (WNB), a small Midwestern bank is reviewing its service charges and interest­ paying policies on checking accounts. The bank presently has a total of 5,000 checking accounts. Tue bank has found that the average daily balance on all of its personal checking accounts is $550 with a standard deviation of $150. In addition, the average daily balances have been found to be normally distributed. Listed below you will find current balance information on just 20 randomly sampled accounts maintained at WNB.

I	$539	6	$523	11	$535	16	$800
2	575	7	$569	12	$386	17	$545
3	700	8	$565	13	$810	18	$559
4	714	9	$531	14	$550	19	$461
5	546	10	$402	15	$290	20	$560

1) Determine the mean average account balance based upon the sample data.

2) If you were to draw another random sample of 20 observations from the same population, what is the likelihood (probability) that you would find a larger sample mean than the value you calculated in question 1?

3) WNB has conducted some analysis that reveals that approximately 5 percent of its accounts have an average daily balance below $304. Based upon this information, in a randomly drawn sample of 2,000 accounts, what percentage of accounts could be expected to have au average daily balance below $304?

4) Based upon the population data, what percentage of customers carry average daily balances above

$800?

5) Based upon the population data, what is the daily balance level that would you would expect only 25

percent of the customers to exceed?

6) Based upon the population data, what percentage of customers carry average daily balances below

$200?

7) Based upon the population data, what is the daily balance level that would you would expect 90 percent of the customers to exceed?

8) Based upon the population data, what percentage of customers carry average daily balances between

$200 and $700?

9) WNB has conducted some analysis in consideration of invoking minimum balance requirements because some of its clients maintain unprofitable account balances. If WNB is considering a minimum account balance of $127, how many customers would be expected to have a balance below this value?

10) If WNB chose to model the distribution of average daily balances with the discrete distribution shown below, what is the probability of a customer carrying an average daily balance below $751?

daily balance percent of customers               daily balance percent of customers

$1 - $150	0.38%	$551 - $650	24.86%
$151 - $250	1.90%	$651 - $750	15.96%
$251 - $350	6.90%	$751 - $850	6.90%
$351 - $450	15.96%	$851 - $950	1.90%
$451 - $550	24.86%	$951 or more	0.38%

Answer 1

1.) Average sample mean, = sum of all balance / 20

= 558

2.) we need to find if new sample has mean greater than 558

Population mean, = 550

Popultion standard deviation, = 150

n = 20

= 558

Finging z score,

z = (558 - 550) / (150 /

z = 8 /33.55

z = 0.238 = 0.24

Looking in z table,

A z-score of 0.24 has an area of 0.595

so probabaility is 0.595 for sample to have mean greater than 558

4.)

For this Question let's draw a normal curve for population with mean = 550

and standard deviation = 150

Now, shading the area above 800 thecurve looks as below:

To find area we need to calculate z score which is given by

z = (800 - 550) / 150

z = 1.67

For the above z score area is 0.0478

So, perccentage of customers = 4.78%

6.)

et's draw a normal curve for population with mean = 550

and standard deviation = 150

Now, shading the area below 200 thecurve looks as below:

To find area we need to calculate z score which is given by

z = (200- 550) / 150

z = -2.33

For the above z score area is 0.0099

So, perccentage of customers = 0.99%