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Korvikt [17]
2 years ago
14

The average grade for an exam is 74, and the standard deviation is 7. The grades are curved to follow a normal distribution.

Mathematics
1 answer:
olga nikolaevna [1]2 years ago
8 0

Answer:

0.9772 = 97.72% probability that the grade of a randomly selected students score is more than 60.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The average grade for an exam is 74, and the standard deviation is 7.

This means that \mu = 74, \sigma = 7

What is the probability that the grade of a randomly selected students score is more than 60?

This is 1 subtracted by the pvalue of Z when X = 60. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{60 - 74}{7}

Z = -2

Z = -2 has a pvalue of 0.0228

1 - 0.0228 = 0.9772

0.9772 = 97.72% probability that the grade of a randomly selected students score is more than 60.

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