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olga nikolaevna [1]
2 years ago
9

On a normal distribution if IQ test scores, with a mean of 100 and a standard deviation of 15 points, a score of 85 places you a

pproximately in what percentile of the population?A. 16thB. 50thC. 97thD. 76thE. 24th
Mathematics
1 answer:
Natali [406]2 years ago
3 0

Answer:

A. 16th

Step-by-step explanation:

We have been given that on a normal distribution IQ test scores, with a mean of 100 and a standard deviation of 15 points. We are asked to find the percentile for a score of 85.

We will use z-score formula and normal distribution table to answer our given problem.

z=\frac{x-\mu}{\sigma}, where,

z = Z-score,

x = Sample score,

\mu = Mean,

\sigma = Standard deviation.

Upon substituting our given values in z-score formula, we will get:

z=\frac{85-100}{15}

z=\frac{-15}{15}

z=-1

Now, we need to find area under a normal curve that corresponds to z-score of -1 that is P(z.

Using normal distribution table, we will get:

P(z

Let us convert 0.15866 into percentage as:

0.15866\times 100\%=15.866\%\approx 16\%

Therefore, a score of 85 places you approximately in 16th percentile of the population.

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