Use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a random sample of 50 people, the mean body mass index (BMI) was 26.7 and the standard deviation was 6.06.

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**Question:**

Use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results.

In a random sample of 50 people, the mean body mass index (BMI) was 26.7 and the standard deviation was 6.06.

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**Question:**

Which distribution should be used to construct the confidence interval? Choose the correct answer below.

- **A.** Use a normal distribution because the sample is random, the population is normal, and σ is known.
  
- **B.** Use a t-distribution because the sample is random, n ≥ 30, and σ is unknown.
  
- **C.** Use a normal distribution because the sample is random, n ≥ 30, and σ is known.
  
- **D.** Use a t-distribution because the sample is random, the population is normal, and σ is unknown.
  
- **E.** Neither a normal distribution nor a t-distribution can be used because either the sample is not random, or n < 30, and the population is not known to be normal.
Transcribed Image Text:**Question:** Use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a random sample of 50 people, the mean body mass index (BMI) was 26.7 and the standard deviation was 6.06. --- **Question:** Which distribution should be used to construct the confidence interval? Choose the correct answer below. - **A.** Use a normal distribution because the sample is random, the population is normal, and σ is known. - **B.** Use a t-distribution because the sample is random, n ≥ 30, and σ is unknown. - **C.** Use a normal distribution because the sample is random, n ≥ 30, and σ is known. - **D.** Use a t-distribution because the sample is random, the population is normal, and σ is unknown. - **E.** Neither a normal distribution nor a t-distribution can be used because either the sample is not random, or n < 30, and the population is not known to be normal.
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