Question

Suppose that distribution of Math SAT scores for incoming freshman at Etown has a mean of 535 and a standard deviation of 30. What is the probability that the average Math SAT score in a class containing 35 students is between 500 and 550?

Answer 1

Here, μ = 535, σ = 5.0709, x1 = 500 and x2 = 550. We need to compute P(500<= X <= 550). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (500 - 535)/5.0709 = -6.9
z2 = (550 - 535)/5.0709 = 2.96

Therefore, we get
P(500 <= X <= 550) = P((550 - 535)/5.0709) <= z <= (550 - 535)/5.0709)
= P(-6.9 <= z <= 2.96) = P(z <= 2.96) - P(z <= -6.9)
= 0.9985 - 0
= 0.9985