Question

Suppose X is a normal random variable with μ = 60 and σ = 5. Find the values of the following probabilities. (Round your answers to four decimal places.)

(a)    P(X < 65)


(b)    P(X > 46)


(c)    P(58 < X < 67)

You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer 1

a) P( X < 65 ) = P[ (X - )/ < ( 65 -60)/5]

P( X < 65 ) = P( Z < 1)

Using standard normal table

P( X < 65) = 0.8413

b) P( X > 46) = P[ (X - )/ > (46-60)/5]

P( X > 46) = P( Z > -2.80)

P( X > 46 ) = 1 - P( Z < -2.80)

P( X > 46) = 1 - 0.0026

P( X > 46) = 0.9974

c) P(58 < X < 67) = P[ (58 - 60)/5<(X - )/< (67-60)/5]

P(58 < X < 67) = P( -0.40 < Z < 1.4)

= P( Z < 1.4) - P( -0.4)

= 0.9192 - 0.3446

P( 58 < X < 67) = 0.5746