Question

A recently admitted class of graduate students at a large state university has a mean GRE verbal score of 650 with a standard deviation of 50. The scores are reasonably normally distributed. Five students have parents who happen to be on the board of trustees, and these students were admitted with a mean GRE score of 490. Should the local newspaper editor write a scathing editorial about favoritism?

Answer 1

Answer:

The answer is below

Step-by-step explanation:

The z score is a score used to determine the number of standard deviations by which the raw score is above or below the mean, it is given by the equation:

$z=\frac{x-\mu}{\sigma} \\\\\mu=mean, \sigma=standard\ deviation,x=raw\ score\\\\for\ a\ sample\ n:\\\\z=\frac{x-\mu}{\sigma/\sqrt{n} }$

Given that μ = 650, σ = 50. To find the probability that 5 students who have a mean of 490, we use:

$z=\frac{x-\mu}{\sigma/\sqrt{n} } =\frac{490-650}{50/\sqrt{5} } =-7.16$

From the normal distribution table, P(x < 490) = P(Z < -7.16) = 0.0001 = 0.01%

Since only a small percentage of people score about 490, hence the local newspaper editor should write a scathing editorial about favoritism