Question

an automotive service company has franchises in two different parts of a city. the number of oil changes made daily, for 25 days, is given below. complete parts a) through f) below.

east store
37, 58, 27, 32, 43
20, 37, 29, 25, 32
44, 29, 54, 38, 54
39, 69, 37, 44, 46
15, 27, 51, 42, 46

west store
42, 43, 43, 40, 34
42, 37, 39, 42, 32
39, 41, 42, 36, 48
28, 30, 37, 43, 33
36, 49, 31, 42, 46

b. the east store appears to have a greater mean since its histogram is centered further to the right than the west stores histogram is.
c. the stores appear to have approximately the same mean since both histograms are centered around the same point.
d. it is impossible to make an inference about the means from the histograms alone.

d) using the histogram, determine which store appears to have the greater standard deviation. explain.
a. the west store appears to have a greater standard deviation since its histogram is wider than the east stores histogram is.
b. the east store appears to have a greater standard deviation since its histogram is wider than the west stores histogram is.
c. the stores appear to have approximately the same standard deviation since both histograms have the same width.
d. it is impossible to make an inference about the standard deviations from the histograms alone.

e) calculate the mean for each store and determine whether your answer in part c) was correct.
the mean for the east store is 39.00 and the mean for the west store is 39.00. these values are consistent with the answer in part c).
(round to two decimal places as needed.)

f) calculate the standard deviation for each store and determine whether your answer in part d) was correct.
the standard deviation for the east store is and the standard deviation for the west store is . these values consistent with the answer in part d).
(round to two decimal places as needed.)

Explanation:

Compare standard deviations visually

Using the Sample Standard Deviation knowledge point
The East store's data ranges from 15 to 69 (range of 54), while the West store's data ranges from 28 to 49 (range of 21). The East store's distribution is much wider and more spread out than the West store's distribution. Therefore, the East store appears to have a greater standard deviation because its histogram is wider.
This corresponds to option B: "The East store appears to have a greater standard deviation since its histogram is wider than the West store's histogram is."

Verify mean calculations

Using the Mean Calculation knowledge point
The problem states that the mean for the East store is \(39.00\) and the mean for the West store is \(39.00\).
These values are consistent with the visual comparison in part c, where both histograms are centered around the same point (39).
Thus, the dropdown selection is "are".

Calculate East store standard deviation

Using the Sample Standard Deviation knowledge point

$$
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$$

Calculate West store standard deviation

Using the Sample Standard Deviation knowledge point

$$
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$$

Compare calculated standard deviations

Using the Sample Standard Deviation knowledge point
Since \(11.49 > 5.00\), the East store has a larger standard deviation, which matches our visual estimation in part d.
Thus, these values are consistent with the answer in part d.
The dropdown selection is "are".

Answer:

Question 1

Using the histogram, determine which store appears to have the greater standard deviation. Explain.

• A. The West store appears to have a greater standard deviation since its histogram is wider than the East store's histogram is.
• B. The East store appears to have a greater standard deviation since its histogram is wider than the West store's histogram is. (Correct answer)
• C. The stores appear to have approximately the same standard deviation since both histograms have the same width.
• D. It is impossible to make an inference about the standard deviations from the histograms alone.

Question 2

The mean for the East store is \(39.00\) and the mean for the West store is \(39.00\). These values <blank>are</blank> consistent with the answer in part c).

Question 3

The standard deviation for the East store is <blank>\(11.49\)</blank> and the standard deviation for the West store is <blank>\(5.00\)</blank>.

Question 4

These values <blank>are</blank> consistent with the answer in part d).