Question

At a high school, past records indicate that the MSAT scores of students have a mean of 510 and a standard deviation of 90. One hundred students in the high school are to take the test. What is the probability that the sample mean score will be (a) within 10 of the population mean? (b) less than 500? (c) between 495 and 515 (d) more than 530?

Answer 1

Solution :

= / n = 90 / 100 = 90 / 10 = 9

(a)

= P[ -10 / 9 < ( - ) / < 10 / 9)]

= P(-1.11 < Z < 1.11)

= P(Z < 1.11) - P(Z < -1.11)

= 0.733

(b)

P( < 500) = P(( - ) / < (500 - 510) / 9)

= P(z < -1.11)

= 0.1335

(c)

= P[ (495 - 510) / 9 < ( - ) / < (515 - 510) / 9)]

= P(-1.67 < Z < 0.56)

= P(Z < 0.56) - P(Z < -1.67)

= 0.6648

(d)

P( > 530) = 1 - P( < 530)

= 1 - P[( - ) / < (530 - 510) / 9]

= 1 - P(z < 2.22)

= 0.0132