Question

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Explanation:

Extract the given values

Using the Standard Deviation Interpretation and Data Variability Analysis knowledge points
The problem describes pizza delivery times for two different shops:

• First shop: Mean delivery time \(\mu_1 = 45\text{ minutes}\), standard deviation \(\sigma_1 = 3\text{ minutes}\).
• Second shop: Mean delivery time \(\mu_2 = 43\text{ minutes}\), standard deviation \(\sigma_2 = 20\text{ minutes}\).

Compare the means and variations

Using the Standard Deviation Interpretation and Data Variability Analysis knowledge points

• Means: The mean delivery times are very close (\(45\text{ minutes}\) vs. \(43\text{ minutes}\)), so they are nearly equal.
• Variations: The standard deviation measures variability. The first shop has a very low standard deviation (\(\sigma_1 = 3\)), while the second shop has a much larger standard deviation (\(\sigma_2 = 20\)). Thus, the variation is significantly greater for the second shop than for the first.
• This matches option A for the first question.

Evaluate the best shop to order from

Using the Standard Deviation Interpretation and Data Variability Analysis knowledge points

• A lower standard deviation means the delivery times are highly consistent and predictable (more reliable).
• The first shop has a standard deviation of only \(3\text{ minutes}\), meaning most deliveries arrive very close to the \(45\)-minute mark.
• The second shop has a standard deviation of \(20\text{ minutes}\), meaning a delivery could easily take much longer (e.g., over an hour) or much shorter.
• Therefore, the first shop is more reliable because it has a lower standard deviation.
• This matches option D for the second question.

Answer:

Question 1

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

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)