## Question 390:

1

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I believe you're looking for the probability between two points in a normal distribution. To do so we calculate z-scores for both points of interest and subtract the smaller area from the larger area. To do so we need the mean and standard deviation, you've provided the mean of 50, but no standard deviation. I'll use a standard deviation of 10 to illustrate how to solve this, then when you find the standard deviation you can change the values and get the answer.

First, find the z-scores for each data-point by subtract each from the mean and dividing that result by the standard deviation.

1. (47-50)/10 = a z-score of -.3. Looking up the area under the normal curve up to this point using the z-score to percentile calculator provides an area of  38.2%
2. (32-50)/10 = a z-score of -1.8. Looking up the area under the normal curve up to this point using the z-score to percentile calculator provides an area of 3.6%

We now subtract the large from the smaller (38.2-3.6) = 34.6. Or about 35% of scores fall between the scores of 32 and 47 given a normal population with a mean of 50 and standard deviation of 10.

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