Questions: Which of the following are true statements about the pizza delivery times? (Select all that apply.) About 68% of deliveries are between 24 and 32 minutes. On average, a delivery taking less than 26 minutes is equally as likely as a delivery taking more than 30 minutes. On average, a delivery taking less than 25 minutes is more common than a delivery taking more than 35 minutes. About 95% of deliveries are between 20 and 36 minutes.

Which of the following are true statements about the pizza delivery times? (Select all that apply.) About 68% of deliveries are between 24 and 32 minutes. On average, a delivery taking less than 26 minutes is equally as likely as a delivery taking more than 30 minutes. On average, a delivery taking less than 25 minutes is more common than a delivery taking more than 35 minutes. About 95% of deliveries are between 20 and 36 minutes.
Transcript text: Which of the following are true statements about the pizza delivery times? (Select all that apply.) About $68 \%$ of deliveries are between 24 and 32 minutes. On average, a delivery taking less than 26 minutes is equally as likely as a delivery taking more than 30 minutes. On average, a delivery taking less than 25 minutes is more common than a delivery taking more than 35 minutes. About 95\% of deliveries are between 20 and 36 minutes.
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Solution

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Solution Steps

Step 1: Understanding the Normal Distribution

The image shows a normal distribution curve with standard deviations marked on the x-axis. The mean (μ) is at 0, and the standard deviations (σ) are marked as -3σ, -2σ, -1σ, 1σ, 2σ, and 3σ.

Step 2: Interpreting the Statements

We need to determine which statements about the pizza delivery times are true based on the properties of the normal distribution.

Step 3: Evaluating Each Statement

  1. About 68% of deliveries are between 24 and 32 minutes.

    • In a normal distribution, approximately 68% of the data falls within one standard deviation (±1σ) of the mean. If the mean delivery time is 28 minutes (midpoint of 24 and 32), this statement is true.

  2. On average, a delivery taking less than 26 minutes is equally as likely as a delivery taking more than 30 minutes.

    • This statement is not true. In a normal distribution, the probability of a delivery time less than the mean (28 minutes) is equal to the probability of a delivery time more than the mean. Since 26 and 30 minutes are not equidistant from the mean, this statement is false.

  3. On average, a delivery taking less than 25 minutes is more common than a delivery taking more than 35 minutes.

    • This statement is true. In a normal distribution, values closer to the mean are more common. Since 25 minutes is closer to the mean (28 minutes) than 35 minutes, deliveries taking less than 25 minutes are more common.

Final Answer

  1. True
  2. False
  3. True
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