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

Solution:

Given, the Normal distribution with,

   = 70

= 6

Find P(Between 70 and 9)

= P(70< x< 90)

= P(X < 90) - P(X < 70)

=  P[(X - )/ <  (90 - 70)/6] -   P[(X - )/ <  (70 - 70)/6]

= P[Z < 3.33] - P[Z < 0.00]

= 0.9996 - 0.5000 ..Use z table

= 0.4996

P(Between 70 and 9) = 0.4996