Question

Suppose that, for a certain mathematics class, the scores are normally distributed with a mean of 75 and a standard deviation of 6. The teacher wishes to give A's to the top 5% of the students and F's to the bottom 5%. The next 15% in either direction will be given B's and D's, with the other students receiving C's.

What is the cumulative distribution?

Answer 1

Answer on Question #76564 – Math – Statistics and Probability

Question

Suppose that, for a certain mathematics class, the scores are normally distributed with a mean of 75 and a standard deviation of 6. The teacher wishes to give A's to the top 5% of the students and F's to the bottom 5%. The next 15% in either direction will be given B's and D's, with the other students receiving C's.

What is the cumulative distribution?

Solution

The z-scores associated with the given probability values can be determined from the standard normal table or calculated using the technology (function NORM.S.INV() of MS Excel).

A z-score is converted into data score as follows.

$$x = \mu + z \sigma$$

The results are summarized in the table.

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