Question

Assume that all SAT scores are normally distributed with a mean µ = 1518 and a standard deviation σ = 325. If 100 SAT scores (n = 100) are randomly selected, find the probability that the scores will have an average less than 1500.

TIP: Make the appropriate z-score conversion 1st, and then use Table A-2 (Table V) to find the answer.

Assume that all SAT scores are normally distributed with a mean µ = 1518 and a standard deviation σ = 325. If 100 SAT scores (n = 100) are randomly selected, find the probability that the scores will have an average less than 1500. TIP: Make the appropriate z-score conversion 1st, and then use Table A-2 (Table V) to find the answer.

A. 0.2912

B. -0.55

C. 0.55

D. 0.7088

Answer 1

Solution :

Given that ,

$\mu$
_T
= 1518

$\sigma$
_T
= $\sigma$ / $\sqrt$ n = 325 / $\sqrt$ 100 = 32.5

P(
T
< 1500) = P((
T
- $\mu$
_T
) / $\sigma$
_T
< (1500 - 1518) / 32.5)

= P(z < -0.55)

Using z table

= 0.2912

correct option is = A