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Lelu [443]
2 years ago
10

John finds that there is a scholarship available to all personals scoring in the top 5% on the ACT test. If the mean score on th

e ACT is 21 with a standard deviation of 4.7, what score does he need in order to qualify for the scholarship
Mathematics
1 answer:
Setler79 [48]2 years ago
5 0

Answer:

He needs a score of 28.7315 to qualify for the scholarship

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 mean score on the ACT is 21 with a standard deviation of 4.7

This means that \mu = 21, \sigma = 4.7

What score does he need in order to qualify for the scholarship?

The top 5%, so the 100 - 5 = 95th percentile, which is X when Z has a p-value of 0.95, so X when Z = 1.645.

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

1.645 = \frac{X - 21}{4.7}

X - 21 = 4.7*1.645

X = 28.7315

He needs a score of 28.7315 to qualify for the scholarship

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x = 9

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