Ommy Teacher wants to analyze the weights of the students at his school. He knows the weight of the students is normally distributed so he can use the standard normal distribution. He measures the weight of 100 randomly selected students in the school. He finds the mean is 80 pounds and the standard deviation is 8 pounds.

Out of 100 students, how many should weigh between 64 and 96 pounds?

Question

Cristian Tyler

Mathematics

21 June, 13:44

Ommy Teacher wants to analyze the weights of the students at his school. He knows the weight of the students is normally distributed so he can use the standard normal distribution. He measures the weight of 100 randomly selected students in the school. He finds the mean is 80 pounds and the standard deviation is 8 pounds.

Out of 100 students, how many should weigh between 64 and 96 pounds?

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Answers (1)

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Jonathon · Answer 1

We first determine the z-scores for the given x-values of 64 and 96.

For x = 64: z = (64 - 80) / 8 = - 2

For x = 96: z = (96 - 80) / 8 = 2

Therefore we find the probability that - 2 < z < 2, which is around 0.95. Therefore, out of 100 students, approximately 100 (0.95) = 95 students will weigh between 64 and 96 pounds.