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Scores on a test are normally distributed with a mean of 80 and a standard deviation of 5. what is the probability that a randomly selected student scored between 85 and 91?

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Because the mean, standard deviation, and student scores are given, you use the formula:
z = \frac{x - xbar} {sd} to determine the z score for each scores. Then look up these z scores in a cumulative z score table, to find the probabilities associated with each of them. Subtract the lower probability from the higher probability and find the final answer.

For this problem:
z_(91) = 2.2 and
z_(85) = 1.

The probabilities associated with these z scores are: 0.9861 and 0.8413 respectively. Therefore the probability that a randomly selected student scores between 85 and 90 = 0.9861 - 0.8413 = 0.1448 or 14.48 %

Jeff Negus
Tutoring In An Instant (TutIAI)
User Fabis
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