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Suppose that scores on a recent statistics exam were normally distributed, that students in the 80th percentile of scores earned 85 points, and that students in the 30th percentile of scores earned 65 points. What was the mean of all exam scores in the class?.



Answer :

The mean of all exam scores in the class is found = 71

Normally distribution

A normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme.

While data points are referred to as x in a normal distribution, they are called z or z-scores in the z-distribution. A z-score is a standard score that tells you how many standard deviations away from the mean an individual value (x) lies: A positive z-score means that your x-value is greater than the mean.

The z-score is found by;

z = (x - μ)/σ

x =  sample mean

μ =  mean score

σ =  standard deviation

Now, from this,

x = zσ + μ

For p = 80th percentile= 0.8, see z value from z score table.

z = 0.85

x = 85 points

85 = 0.85σ +  μ  .....eq 1

For p = 30% = 0.3, see the z value from the z score table.

z = -0.3802

x = 65

65 = -0.3802σ +  μ  .....eq 2

Solving eq 1 and 2.

σ = 16.25

Put in eq 1

μ = 71.19

μ = 71

Thus, the mean of all exam scores in the class is found = 71

To learn more about Normal Distribution visit:

brainly.com/question/13759327

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