Question

Suppose that the mean score for the mathematics test cited in Problem 7 is 610. What is the probability that a random sample of 225 students will have a mean score of more than 625

Answer 1

Reference from question 7 :

Standard deviation (σ) = 120

Standard Error = 8

Answer:

0.0304

Explanation:

Sample size (n) = 225

Sample mean = 625

Population mean = 610

Using the relation :

Z = (sample mean - population mean) / σ/√n

Z = (625 - 610) / (120/√225)

Z = 15 / (120/15)

Z = 15 / 8

Z = 1.875

P(mean score of more than 625)

P(Z > 1.875) = 1 - p(Z < 1.875)

p(Z < 1.875) = 0.9696

P(Z > 1.875) = 1 - p(Z < 1.875) = 1 - 0.9696 = 0.0304