Question

3. The average sale per customer at a department store is $120.00 with a standard deviation of $10.00.  

According to the Empirical Rule, the percentage of sales between

$90.00 and $150.00 would be   __________________

Using Chebyshev’s Theorem, the upper and lower limits for 75% of the data values =

_________to ___________.

c)    If a customer spends $160.00, which of the following is correct?

a) It is an outlier because it’s more than 3 standard deviations below the mean.

b) It is an outlier because it’s more than 3 standard deviations above the mean.

c) It is not an outlier.

d) None of the above is correct.

Answer 1

Solution:

Given: Mean =

Standard deviation =

Part a)

According to the Empirical Rule, the percentage of sales between $90.00 and $150.00 would be:

Find k for 90 and for 150.

Thus number of standard deviation = k = 3 for 90.00 and 150.00

Thus according to empirical rule 99.7% of the data fall within 3 standard deviation from the mean.

Thus answer is: 99.7%

Part b) Using Chebyshev’s Theorem, the upper and lower limits for 75% of the data values

According to Chebyshev’s Theorem at least % of the data fall within the k standard deviation from the mean.

Thus we have: = 75%

then

Thus use following formula:

and

the upper and lower limits for 75% of the data values = 100.00 to 140.00

Part c) If a customer spends $160.00, which of the following is correct?

We know : Mean + 3* SD = 120.00 + 3*10.00 = 120.00 + 30.00 = 150.00

Thus x = 160.00 is more than 3 standard deviations above the mean.

Thus correct answer is:
b) It is an outlier because it’s more than 3 standard deviations above the mean.