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andrew11 [14]
3 years ago
14

A community college has a math placement exam that has a mean of 65 and a standard deviation of 8.2. If a student takes the exam

and scores in the lower 2.5%, they are eligible for a free intensive course to help them succeed in their math class. Assume that the exam has a normal distribution. What is the score that cuts off the bottom 2.5%
Mathematics
2 answers:
Marat540 [252]3 years ago
8 0

Answer:

The score that cuts off the bottom 2.5% is 48.93.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 65, \sigma = 8.2

What is the score that cuts off the bottom 2.5%

This is X when Z has a pvalue of 0.025, so X when Z = -1.96.

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

-1.96 = \frac{X - 65}{8.2}

X - 65 = -1.96*8.2

X = 48.93

The score that cuts off the bottom 2.5% is 48.93.

Umnica [9.8K]3 years ago
6 0

Answer:

The score that cuts off the bottom 2.5% is 48.93.

Step-by-step explanation:

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