Question

Calculate the following probabilities using the standard normal distribution. (Round your answers to four decimal places.)

(a)    

P(0.0 ≤ Z ≤ 1.4)

(b)    

P(−0.9 ≤ Z ≤ 0.0)

(c)    

P(0.0 ≤ Z ≤ 1.47)

(d)    

P(0.7 ≤ Z ≤ 1.57)

(e)    

P(−2.09 ≤ Z ≤ −1.75)

(f)    

P(−0.02 ≤ Z ≤ 3.58)

(g)    

P(Z ≥ 2.80)

(h)    

P(Z ≤ 1.61)

(i)    

P(Z ≥ 5)

(j)    

P(Z ≥ −8)

Answer 1

The Probabilities are solved using R-code; here pnorm is the function which returns the cdf of a Normal distribution and assumes the distribution to be standard normal if no mean and variance are mentioned.

The R-code and output are attached below.