Question

after recording the pizza delivery times for two different pizza shops, you conclude that one pizza shop has a mean delivery time of 45 minutes with a standard deviation of 4 minutes. the other shop has a mean delivery time of 43 minutes with a standard deviation of 22 minutes. interpret these figures. if you liked the pizzas from both shops equally well, which one would you order from? why?

interpret these figures. choose the correct answer below.
a. both the means and the variations are nearly equal.
b. the means are nearly equal, but the variation is significantly greater for the second shop than for the first.
c. the means are nearly equal, but the variation is significantly lower for the second shop than for the first.
d. the variations are nearly equal, but the mean is greater for the first shop than for the second.

if you liked the pizzas from both shops equally well, which one would you order from? why? choose the correct answer below.
a. choose the second shop. the delivery time is more reliable because it has a larger standard deviation.
b. choose the second shop. the delivery time is more reliable because it has a larger mean.
c. choose the first shop. the delivery time is more reliable because it has a lower mean.
d. choose the first shop. the delivery time is more reliable because it has a lower standard deviation.

Explanation:

Compare the means and standard deviations

Using the Standard Deviation Interpretation and Data Variability Analysis knowledge points

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The means \(45\) and \(43\) are nearly equal, but the standard deviation of the second shop (\(22\)) is significantly greater than that of the first shop (\(4\)).

Determine the optimal ordering choice

Using the Standard Deviation Interpretation and Data Variability Analysis knowledge points

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A lower standard deviation means the delivery times are more consistent and reliable around the mean, making the first shop the preferred choice.

Answer:

Question 1

• (A) Both the means and the variations are nearly equal.
• (B) The means are nearly equal, but the variation is significantly greater for the second shop than for the first. (Correct answer)
• (C) The means are nearly equal, but the variation is significantly lower for the second shop than for the first.
• (D) The variations are nearly equal, but the mean is greater for the first shop than for the second.

Question 2

• (A) Choose the second shop. The delivery time is more reliable because it has a larger standard deviation.
• (B) Choose the second shop. The delivery time is more reliable because it has a larger mean.
• (C) Choose the first shop. The delivery time is more reliable because it has a lower mean.
• (D) Choose the first shop. The delivery time is more reliable because it has a lower standard deviation. (Correct answer)