Question

"Suppose exam scores are normally distributed with a mean of 70 and a standard deviation of 6. The probability that someone scores between a 70 and a 90 is:"

Answer 1

The probability is 0.40824

Explanation:

To find this probability, we shall start with finding the z-scores of each

Mathematically;

z-score = (x-mean)/SD

for 70

z = (70-70)/6 = 0

For 90

z = (90-70)/6 = 20/6 = 10/3 = 1.33

So the probability we want to find is;

P(0 < x < 1.33)

we can use the standard normal distribution to get this;

Mathematically, that would be;

P( x <1.33) - P( x < 0)

Using the standard normal distribution table, we have;

P = 0.40824