Question

The final exam scores of students taking a statistics course are normally distributed with a population mean of 72 and a population standard deviation of 8. If a student taking this statistics course is randomly selected, what is the probability that his/her final exam score is between 60 and 84? A .4332 .9332 C .8664 .1336 Submit Answer

Answer 1

Here, μ = 72, σ = 8, x1 = 60 and x2 = 84. We need to compute P(60<= X <= 84). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (60 - 72)/8 = -1.5
z2 = (84 - 72)/8 = 1.5

Therefore, we get
P(60 <= X <= 84) = P((84 - 72)/8) <= z <= (84 - 72)/8)
= P(-1.5 <= z <= 1.5) = P(z <= 1.5) - P(z <= -1.5)
= 0.9332 - 0.0668
= 0.8664

Option C