Assume scores on a recent national statistics exam were norm

Assume scores on a recent national statistics exam were normally distributed with a mean of 74 and a standard deviation of 6. Find the probability that a randomly selected student score more than 80 points? If the top 2.5% of test scores recurveerit awards, what is the lowest eligible for an award?

Solution

m =74

sd = s = 6

x1 = 80

P(x>80) = 1 - P(x<80)

P(x>80) = 1 - P(z<(80-74)/6)

P(x>80) = 1 - P(z<1)

P(x>80) = 1 - 0.8413

P(x>80) = 0.1587

2.

P(x>x2) = 0.025

P(x<x2) = 1 - 0.025

P(x<x2) = 0.975

P(z<z2) = 0.975

z2 = 1.96

x-m = 1.96 * s

x = 74 + 1.96 * 6

x = 85.76