Question

Find the following probabilities for Verbal SAT test scores X, for which the mean is 500 and the standard deviation is 100. Assume that SAT scores are described by a normal curve.

a. P(X<500).

b. P(X<650).

c. P(X>700).

d. P(500<X<700).

Answer 1

Mean=500, SD=100.

Z=(X-500)/100. P(Z) tables give the area (probability) to the left of X, that is, X≤n. To find the area corresponding to X≥n, subtract from 1 (area to the right).

a. P(X≤500). Half the test scores are below the mean and half are above.

Z=0 so probability is 0.5 or 50%.

b. P(X≤650).

Z=1.5. P(Z)=0.933 or 93.3% approx.

c. P(X≥700).

Z=2. P(Z)=0.977 approx. So P(X≥700)=1-0.977=0.023 or 2.3%.

d. P(500≤X≤700).

Probability=0.977-0.500=0.477 or 47.7%. This is close to 50% which is to be expected.