High School

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The mean weight of 1000 students at a certain high school is 140 pounds, and the variance is 100 pounds. Assuming that the weights are normally distributed, how many students weigh:

a. Between 120 and 145 pounds?

b. More than 150 pounds?

Answer :

Using the mean weight and variance, we calculate the z-scores for the given weights and use a normal distribution table to determine the proportion of students within the specified weight ranges. This proportion is then multiplied by the total number of students to estimate the number of students who weigh between 120 and 145 pounds, and more than 150 pounds.

To solve this problem, we can use the properties of the normal distribution. Given a mean a. To find the number of students who weigh between 120 and 145 pounds, we can calculate the z-scores for these weights:

For 120 pounds: z = (120 - 140) / 10 = -2

For 145 pounds: z = (145 - 140) / 10 = 0.5

Using a standard normal distribution table, we find the probabilities corresponding to these z-scores and then find the difference to get the proportion of students within this range.

b. To find the number of students who weigh more than 150 pounds, we calculate the z-score for 150 pounds:

z = (150 - 140) / 10 = 1

Then, we find the probability corresponding to this z-score in the standard normal distribution table and subtract this value from 1 to find the proportion of students that weigh more than 150 pounds. Multiplying this proportion by 1000 gives us the estimated number of students.

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