Question

Suppose the scores of students on an exam are Normally distributed with a mean of 405 and a standard deviation of 69. Then approximately 99.7% of the exam scores lie between the numbers ____ and ____ such that the mean is halfway between these two integers.

Answer 1

Answer:

 198 and 612

Step-by-step explanation:

We are given that the scores are normally distributed.

The mean of the data is 405.

The standard deviation of this data is 69.

Empirical rule states that for a normally distributed data that

• about 68% data lies between $\mu \pm 1\sigma$ that is one standard deviation from mean.

• about 95% data lies between $\mu \pm 2\sigma$ that is one standard deviation from mean.

• about 99.7% data lies between $\mu \pm 3\sigma$ that is one standard deviation from mean.

Thus, 99.7% of data will lie between $405 \pm 3(69)$ that is it will lie in the range (198,612)