Question

In: Statistics and Probability

Scores on a national exam vary normally with a mean of 400 and standard deviation of...

Scores on a national exam vary normally with a mean of 400 and standard deviation of 75.

a. What must a student score to be in the 90th percentile?

b. if 16 student take the exam, what is the probabiltiy that their mean score is at most 390?

Please make sure you explain and show your work, as to how you got the standard devation of 75?

Expert Solution

Solution:

We are given that scores on a national exam vary normally with mean and standard deviation given:

a. What must a student score to be in the 90th percentile?

Answer: We have to first find the z-score corresponding to area=0.90. Using the standard normal table, we have:

Now using the Z-score formula, we have:

b. if 16 students take the exam, what is the probability that their mean score is at most 390?

Answer: We have to find

Using the z-score formula, we have:

Now using the standard normal table, we have:

orchestra answered 1 year ago

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