Question

A normal random variable x has mean ? = 1.7 and standard deviation ? = 0.12. Find the probability associated with each of the following intervals. (Round your answers to four decimal places.)

(a)    

1.00 < x < 1.40

(b)    

x > 1.34

(c)    

1.25 < x < 1.50

Answer 1

a) P(1 < X < 1.4)

= P((1 - )/ < (X - )/ < (1.4 - )/)

= P((1 - 1.7)/0.12 < Z < (1.4 - 1.7)/0.12)

= P(-5.83 < Z < -2.5)

= P(Z < -2.5) - P(Z < -5.83)

= 0.0062 - 0

= 0.0062

b) P(X > 1.34)

= P((X - )/ > (1.34 - )/)

= P(Z > (1.34 - 1.7)/0.12)

= P(Z > -3)

= 1 - P(Z < -3)

= 1 - 0.0013

= 0.9987

c) P(1.25 < X < 1.5)

= P((1.25 - )/ < (X - )/ < (1.5 - )/)

= P((1.25 - 1.7)/0.12 < Z < (1.5 - 1.7)/0.12)

= P(-3.75 < Z < -1.67)

= P(Z < -1.67) - P(Z < -3.75)

= 0.0475 - 0

= 0.0475