High School

The mean time to assemble a piece of furniture is 52 minutes. Suppose the assembly times are normally distributed with a standard deviation of 4.3 minutes.

Between what two times do 99.7% of the assembly times fall? Use the Empirical Rule.

A. 47.7 minutes and 56.3 minutes
B. 43.4 minutes and 60.6 minutes
C. 39.1 minutes and 64.9 minutes
D. 39.1 minutes and 56.3 minutes

Answer :

Final answer:

Between 99.7% of the assembly times fall between 39.1 minutes and 64.9 minutes.

Explanation:

To find the range within which 99.7% of the assembly times fall, we can use the Empirical Rule.

The Empirical Rule states that for a normal distribution, approximately 68% of the values fall within one standard deviation of the mean, 95% fall within two standard deviations, and 99.7% fall within three standard deviations.

In this case, the mean is 52 minutes and the standard deviation is 4.3 minutes. Three standard deviations above and below the mean would give us a range of:

  • 52 minutes - (3 * 4.3 minutes) = 52 minutes - 12.9 minutes = 39.1 minutes
  • 52 minutes + (3 * 4.3 minutes) = 52 minutes + 12.9 minutes = 64.9 minutes

Therefore, between 99.7% of the assembly times fall between 39.1 minutes and 64.9 minutes.

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