Question

Find the following probabilities. (Round your answers to four decimal places.)

(a)    p(0 < z < 1.44)


(b)    p(1.03 < z < 1.69)


(c)    p(−0.87 < z < 1.72)


(d)    p(z < −2.07)


(e)    p(−2.32 < z < −1.17)


(f)    p(z < 1.52)

Answer 1

Solution :

Given that,  

Using standard normal table ,

(a)

P(0 < z < 1.44)

= P(z < 1.44) - P(z < 0)

= 0.9251 - 0.5

= 0.4251

P(0 < z < 1.44) = 0.4251

(b)

P(1.03 < z < 1.69)

= P(z < 1.69) - P(z < 1.03)

= 0.9545 - 0.8485

= 0.106

P(1.03 < z < 1.69) = 0.106

(c)

P(-0.87 < z < 1.72)

= P(z < 1.72) - P(z < -0.87)

= 0.9573 - 0.1922

= 0.7651

P(-0.87 < z < 1.72) = 0.7651

(d)

P(z < -2.07) = 0.0192

(e)

P(-2.32 < z < -1.17

= P(z < -1.17) - P(z < -2.32)

= 0.121 - 0.0102

= 0.1108

P(-2.32 < z < -1.17 = 0.1108

(f)

P(z < 1.52) = 0.9357