Question

What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test (to 4 decimals)?

Answer 1

Answer:

0.658 is the probability that a sample 90 test takers will provide a sample mean test score within 10 points of the population mean of 502.

Step-by-step explanation:

The following information is missing:

The standard deviation of population is 100.

We are given the following information in the question:

Population mean, μ = 502

Standard Deviation, σ = 100

Sample size, n  = 90

Standard error =

$\dfrac{\sigma}{\sqrt{n}} = \dfrac{100}{\sqrt{90}} = 10.54$

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(test score within 10 points)

$P(492 \leq x \leq 512) \\\\= P(\displaystyle\frac{492 - 502}{10.54} \leq z \leq \displaystyle\frac{512-502}{10.54}) \\\\= P(-0.9487 \leq z \leq 0.9487)\\= P(z \leq 0.9487) - P(z < -0.9487)\\= 0.829 -0.171 = 0.658 = 65.8\%$

$P(492 \leq x \leq 512) = 65.8\%$

0.658 is the probability that a sample 90 test takers will provide a sample mean test score within 10 points of the population mean of 502.