In order to control costs, a company wishes to study the amount of money its sal
ID: 3043298 • Letter: I
Question
In order to control costs, a company wishes to study the amount of money its sales force spends entertaining clients. The following is a random sample of six entertainment expenses (dinner costs for four people) from expense reports submitted by members of the sales force.
(b) Assuming that the distribution of entertainment expenses is approximately normally distributed, calculate estimates of tolerance intervals containing 68.26 percent, 95.44 percent, and 99.73 percent of all entertainment expenses by the sales force. (Round intermediate calculations and final answers to 2 decimals.)
(c) If a member of the sales force submits an entertainment expense (dinner cost for four) of $390, should this expense be considered unusually high (and possibly worthy of investigation by the company)? Explain your answer.
(d) Compute and interpret the z-score for each of the six entertainment expenses. (Round z-score calculations to 2 decimal places. Negative amounts should be indicated by a minus sign.)
$ 357 $ 332 $ 309 $ 345 $ 325 $ 339Explanation / Answer
Answer:
In order to control costs, a company wishes to study the amount of money its sales force spends entertaining clients. The following is a random sample of six entertainment expenses (dinner costs for four people) from expense reports submitted by members of the sales force.
$
357
$
332
$
309
$
345
$
325
$
339
(a) Calculate , s2, and s for the expense data. (Round your answers to 2 decimal places.)
334.50
s2
276.70
s
16.63
(b) Assuming that the distribution of entertainment expenses is approximately normally distributed, calculate estimates of tolerance intervals containing 68.26 percent, 95.44 percent, and 99.73 percent of all entertainment expenses by the sales force. (Round intermediate calculations and final answers to 2 decimals.)
[ ± s]
[317.87, 351.13]
[ ± 2s]
[301.23, 367.77]
[ ± 3s]
[284.60, 384.40]
(c) If a member of the sales force submits an entertainment expense (dinner cost for four) of $390, should this expense be considered unusually high (and possibly worthy of investigation by the company)? Explain your answer.
Answer:
Yes
No
390 is above 3sd limit.
(d) Compute and interpret the z-score for each of the six entertainment expenses. (Round z-score calculations to 2 decimal places. Negative amounts should be indicated by a minus sign.)
x
z
357
1.35
332
-0.15
309
-1.53
345
0.63
325
-0.57
339
0.27
Descriptive statistics
n
6
mean
334.50
sample standard deviation
16.63
sample variance
276.70
minimum
309
maximum
357
range
48
empirical rule
mean - 1s
317.87
mean + 1s
351.13
percent in interval (68.26%)
66.7%
mean - 2s
301.23
mean + 2s
367.77
percent in interval (95.44%)
100.0%
mean - 3s
284.60
mean + 3s
384.40
$
357
$
332
$
309
$
345
$
325
$
339
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