Question

Given that z is a standard normal random variable, compute the following probabilities. Round your answers to 4 decimal places.

a. P(0 _< z _< 0.51)

b. P( -1.61 _< z _< 0)

c. P( z > 0.30)

d. P( z _> -0.31)

e. P( z < 2.06)

f. P( z _< -0.61)

Answer 1

solution:-

given that z is a standard normal random variable

a. P(0 ≤ z ≤ 0.51) = P(z < 0.51) - P(z < 0)

= 0.6950 - 0.5000

= 0.1950

b. P(-1.61 ≤ z ≤ 0) = P(z < 0) - P(z < -1.61)

= P(z < 0) - (1-P(z < 1.61))

= 0.5 - (1-0.9463)

= 0.4463

c. P(z > 0.30) = 1-P(z < 0.30)

= 1-0.6179

= 0.3821

d. P(z ≥ -0.31) = P(z < 0.31)

= 0.6217

e. P( z < 2.06) = 0.9803

f. P( z ≤ -0.61) = 1-P(z < 0.61)

= 1-0.7291

= 0.2709

note:- these z values from standard normal table