Mrs. smith's reading class can read a mean of 175 words per minute with a standard deviation of 20 words per minute. the top 3% of the class is to receive a special award. assuming that the distribution of words read per minute are normally distributed, what is the minimum number of words per minute a student would have to read in order to get the award?

Question

Mathematics

Trystan Roach

3 June, 08:37

Mrs. smith's reading class can read a mean of 175 words per minute with a standard deviation of 20 words per minute. the top 3% of the class is to receive a special award. assuming that the distribution of words read per minute are normally distributed, what is the minimum number of words per minute a student would have to read in order to get the award?

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Liliana Williams · Answer 1

50% of the class performs above the mean. 47% of the class, above the mean, does not achieve this level.

From a normal curve table, the z-score that corresponds to 47% from the value to the mean is a z-score of 1.88. Since the z-score represents the number of standard deviations, the value we are looking for is 175 words + (20 * 1.88) = 175 + 37.6 = 212.6.

Your entry into the Final Exam Shell should be 213.