Question

1. Consider a standard normal random variable with μ = 0 and standard deviation σ = 1. (Round your answers to four decimal places.)

(a)    P(z < 2) =

(b)    P(z > 1.16) =

(c)    P(−2.31 < z < 2.31) =

(d)    P(z < 1.82) =

2. Find the following probabilities for the standard normal random variable z. (Round your answers to four decimal places.)

(a)    P(−1.49 < z < 0.65) =

(b)    P(0.56 < z < 1.74) =

(c)    P(−1.54 < z < −0.46) =

(d)    P(z > 1.36) =

(e)    P(z < −4.38) =

3. Find a z₀ such that

P(z > z₀) = 0.0268.

(Round your answer to two decimal places.)

z₀ =

(b)Find a z₀ such that

P(z < z₀) = 0.9115.

(Round your answer to two decimal places.)

z₀ =

Answer 1

Refer to the standard normal distribution table shown below.

1) (a) P(Z<2) = 0.9772 (refer to row 2.0 and column 0.00)

(b) P(Z>1.16) = 1 - P(Z<1.16) = 1−0.877=0.123

(c) P(-2.31<Z<2.31) = P ( Z<2.31 )−P (Z<−2.31) = P (Z<2.31 ) - [1−P ( Z<2.31)] = (2*P ( Z<2.31 )) - 1 = (2*0.9896)-1 = 0.9792

(d) P(Z<1.82) = 0.9656 (refer to row 1.8 and column 0.02)

We solve only 4 subparts in one post. Please post again for other solutions.