Question

The final exam scores in a statistics class were normally distributed with a mean of 70 and a standard deviation of 2. If you select a student at random, what is the probability that he scored between a 66 and a 74?

A.2.5%

B.50%

C. 68%

C. 95%

D. none of the above

Answer 1

mean = 70 , s = 2

P(66 < x< 74)

Using central limit theorem,

z = (x - mean)/sigma

= P((66- 70)/2 < z < ( 74 - 70)/2)
= P(-2 < z< 2)
= P(z< 2) - P(z< -2)
= 0.9772 - 0.0228

= 0.9544
= 95.44%

= approx 95%
Option C)