Question

If the random variable X is drawn from a normal population with ?=155 and ?=11, find each of the following:

A. ?(?>168)

Probability =

B. ?(?<136)

Probability =

C. ?(150<?<160)

Probability =

Answer 1

Normal distribution: P(X < A) = P(Z < (A - )/)

= 155

= 11

A. P(X > 168) = 1 - P(X < 168)

= 1 - P(Z < (168 - 155)/11)

= 1 - P(Z < 1.18)

= 1 - 0.8810

= 0.1190

B. P(X < 136) = P(Z < (136 - 155)/11)

= P(Z < -1.73)

= 0.0418

C. P(150 < X < 160) = P(X < 160) - P(X < 150)

= P(Z < (160 - 155)/11) - P(Z < (150 - 155)/11)

= P(Z < 0.45) - P(Z < -0.45)

= 0.6736 - 0.3264

= 0.3472