Question

25 SAT scores are randomly selected from a population of SAT scores that are normally distributed. The population has a mean of 1518 and standard deviation of 325. What is the probability that the selected 25 scores have a mean between 1550 and 1575?

Answer 1

The correct answer is 0.1227

Explanation:

Answer 2

The probability that the selected 25 scores have a mean between 1550 and 1575 will be 0.0316

Explanation:

The population has a Mean
`(\mu)` of 1518 and standard deviation
`(\sigma)` of 325.

Formula for finding z-score is:
`z=(X-\mu)/(\sigma)`

So, the z-scores for the mean between 1550 and 1575 are......

`z(X>1550)=(1550-1518)/(325) \approx 0.10`

`z(X<1575)=(1575-1518)/(325) \approx 0.18`

According to the standard normal distribution table:
`P(Z<0.10)=0.5398` and
`P(Z<0.18)= 0.5714`

Now,

`P(1550<X<1575)\\ \\ =P(Z<0.18)-P(Z<0.10)\\ \\ =0.5714-0.5398\\ \\ =0.0316`

So, the probability that the selected 25 scores have a mean between 1550 and 1575 will be 0.0316