Question

The test scores of 1,200 students are normally distributed with a mean of 83 and a standard deviation of 5.5. Under which interval did approximately 978 students score?

Select one:
a. 72 b. 77.5 c. 83 d. 72

Answer 1

Using the Empirical Rule, it is found that the interval in which approximately 978 students scored was:

A. 72 < x < 88.5.

What does the Empirical Rule state?

It states that, for a normally distributed random variable:

• Approximately 68% of the measures are within 1 standard deviation of the mean.

• Approximately 95% of the measures are within 2 standard deviations of  the mean.

• Approximately 99.7% of the measures are within 3 standard deviations of the mean.

The percentage that 978 is of 1200 is:

978/1200 x 100% = 81.5%.

Considering the symmetry of the normal distribution, two outcomes are possible involving 81.5% of the measures:

• Between one standard deviation below the mean and two above, which in the context of this problem is between 77.5 and 94.

• Between two standard deviations below the mean and one above, which in the context of this problem is between 72 and 88.5, which is option A in this problem.

More can be learned about the Empirical Rule at https://brainly.com/question/24537145

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