An exam is given to all students entering school. The scores are approximately normally distributed with a mean of 100 and a standard deviation of 15

Question

a. What percentage of the students have scores between 85 and 115?

b.What percentage of the students have scores between 70 and 130?

c. What percentage of the students have scores between 55 and 145?

d. What percentage of the students have scores above 115?

Answer 1

You need to find the probability of a score inside any given range and convert that number to a percent.

 

To find the probabilities you need to convert each value in a-d into a z-score and look up those scores in an appropriate normal distribution table; see  https://www.wyzant.com/resources/files/392716/normal_dist_table

 

To convert to z-scores use the transformation:  z = (x-μ) / σ.

 

 

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