Question

The grade point averages of the students in a large statistics class follow a normal distribution with a mean of 3.0 and a standard deviation of 0.25. What is the probability that a randomly sampled student from this class has a GPA of less than 2.95? (hint: you will need to use the table on page 175)

Answer 1

Here, μ = 3, σ = 0.25 and x = 2.95. We need to compute P(X <= 2.95). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (2.95 - 3)/0.25 = -0.2

Therefore,
P(X <= 2.95) = P(z <= (2.95 - 3)/0.25)
= P(z <= -0.2)
= 0.4207