Question

A memory test consists of 35 tasks. Each task is graded on a scale of 1 to 10. The score on the memory test is reported as the sum of the scores of the tasks. The mean score on the tasks is 4.8 with a standard deviation of 3. What is the probability that a randomly selected examinee will score 170 points or less on the memory test?
Carry your intermediate computations to at least four decimal places. Report your result to at least three decimal places.

Answer 1

mean = 4.8 * 35 = 168
std. dev. = 3*sqrt(35) = 17.7482

Here, μ = 168, σ = 17.7482 and x = 170. We need to compute P(X <= 170). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (170 - 168)/17.7482 = 0.11

Therefore,
P(X <= 170) = P(z <= (170 - 168)/17.7482)
= P(z <= 0.11)
= 0.544