Question

3)   Scores on the SAT are normally distributed with a mean of 500 and a standard deviation of 100

1. What is the probability of obtaining a score greater than 640?
2. What is the probability of obtaining a score less than 390?
3. What is the probability of obtaining a score between 725 and 800?
4. What is the probability of obtaining a score either less than 375 or greater than 650?

4) If you obtained a score of 75 on an test, the standard deviation was 12 and you were told you had a score higher than 80 percent of your classmates, what was the mean on the test?

Answer 1

Question 3

Scores on SAT are normally distributed with a mean of 500, and a standard deviation of 100.

So, if X be the random variable denoting the score of a randomly selected student, then X follows normal with a mean of 500 and a standard deviation of 100.

So, we can say that, Z=(X-500)/100 follows standard normal with mean 0 and standard deviation of 1.

Question a)

where, phi is distribution function of the standard normal variate.

Question (b)

Question (c)

Question (d)

Question 4

I obtained a score of 75 on a test; the test had standard deviation of 12.

I have a score higher than 80% of my classmates.

So, let the mean be m.

Now, it is given that

From the standard normal table, we have

So, we can conclude

So, the mean is 64.896.