Problem 3 (30pts) In a recent year, grade 8 Washington State public schools students taking a mathematics assessment test had a mean score of 281 with a standard deviation of 34 4 Possible test scores could range from 0 to 500 Assume that the scores are normally distributed What is the lowest score that still place a student in the top 15 of the scores Fin the probability that a student had a score higher than 350 Find the probability that a student had a score between 250 and 315 If 1500 students are randomly selected, how many would be expected to have a score between 250 and 315 A random sample of 16 students is drawn from this population, what is the probability that the mean score is greater than 300

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Question: Problem 3: (30pts) In a recent year, grade 8 Washington State public schools students taking a mathematics assessment test had a mean score of 281

Problem 3: (30pts)

In a recent year, grade 8 Washington State public schools students taking a mathematics assessment test had a mean score of 281 with a standard deviation of 34.4.

Possible test scores could range from 0 to 500. Assume that the scores are normally distributed.

What is the lowest score that still place a student in the top 15% of the scores?
Fin the probability that a student had a score higher than 350.
Find the probability that a student had a score between 250 and 315.
If 1500 students are randomly selected, how many would be expected to have a score between 250 and 315?
A random sample of 16 students is drawn from this population, what is the probability that the mean score is greater than 300?

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