After recording the pizza delivery times for two different pizza shops, you conclude that one pizza shop has a mean delivery time of 46 minutes with a standard deviation of 5 minutes. The other sho has a mean delivery time of 42 minutes with a standard deviation of 21 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 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.

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We are given two sets of data for delivery times from two pizza shops. Let:

- For the first shop: mean delivery time, $$ \mu_1 = 46 $$ minutes and standard deviation, $$ \sigma_1 = 5 $$ minutes.
- For the second shop: mean delivery time, $$ \mu_2 = 42 $$ minutes and standard deviation, $$ \sigma_2 = 21 $$ minutes.

**Step 1: Interpreting the Means**

The mean delivery time tells us the average time each shop takes to deliver a pizza.

- The first shop has an average of $$ 46 $$ minutes.
- The second shop has an average of $$ 42 $$ minutes.

While the means are close, the difference of $$ 4 $$ minutes is relatively small.

**Step 2: Interpreting the Standard Deviations**

The standard deviation provides information about the variability of the delivery times around the mean.

- For the first shop: $$ \sigma_1 = 5 $$ minutes indicates that most delivery times are close to the $$ 46 $$ minute average.
- For the second shop: $$ \sigma_2 = 21 $$ minutes indicates that the delivery times are highly variable. This means some pizzas might be delivered very quickly, but some might take much longer than the average of $$ 42 $$ minutes.

**Step 3: Making a Decision**

If you like the pizzas equally well, you may prefer reliability in delivery times. The first shop, with its lower standard deviation, provides more consistent delivery performance, even though its average time is slightly longer. On the other hand, the second shop’s high variation introduces a higher risk of long delays, even if its average delivery time is a bit lower.

**Step 4: Choosing the Correct Answer**

The figures show that:

- The means are nearly equal.
- The variation is significantly greater for the second shop than for the first.

Thus, the correct interpretation is:

$$ 	extbf{B. The means are nearly equal, but the variation is significantly greater for the second shop than for the first.} $$
The first pizza shop has a slightly longer average delivery time but is more consistent. The second shop has a shorter average time but delivery times vary a lot. If you prefer reliable delivery, choose the first shop.

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