Question

The mean score on the verbal section of the SAT test was 510 with a standard deviation of 98.

a. If you choose a test result at random, find the probability that the score on this section is greater than 559

a. If you choose a sample of four tests at random, find the probability that the mean of these scores is greater than 559.

Answer 1

Solution :

a.

P(x > 559) = 1 - P(x < 559)

= 1 - P[(x - ) / < (559 - 510) / 98)

= 1 - P(z < 0.5)

= 1 - 0.6915

= 0.3085

Probability = 0.3085

a.

= / n = 98 / 4 = 49

P( > 559) = 1 - P( < 559)

= 1 - P[( - ) / < (559 - 510) / 49]

= 1 - P(z < 1)

= 1 - 0.8413

= 0.1587

Probability = 0.1587