Question

One college class had a total of 80 students. The average score for the class on the last exam was 84.3 with a standard deviation of 5.4. A random sample of 34 students was selected.

a. Calculate the standard error of the mean.

b. What is the probability that the sample mean will be less than 86?

c. What is the probability that the sample mean will be more than 85?

d. What is the probability that the sample mean will be between 83.5 and 85.5?

Answer 1

Solution :

a.

= / n = 5.4 / 34 = 0.9261

b.

P( < 86) = P(( - ) / < (86 - 84.3) / 0.9261)

P(z < 1.84)

= 0.9671

Probability = 0.9671

c.

P( > 85) = 1 - P( < 85)

= 1 - P[( - ) / < (85 - 84.3) / 0.9261]

= 1 - P(z < 0.76)

= 1 - 0.7764

= 0.2236

Probability = 0.2236

d.

= P[(83.5 - 84.3) /0.9261 < ( - ) / < (85.5 - 84.3) / 0.9261)]

= P(-0.86 < Z < 1.30)

= P(Z < 1.30) - P(Z < -0.86)

= 0.9032 - 0.1949

= 0.7083

Probability = 0.7083