Question

Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. (Round your answers to four decimal places.) (a) P(0 ≤ Z ≤ 2.38) .4913 (b) P(0 ≤ Z ≤ 1) .3413 (c) P(−2.70 ≤ Z ≤ 0) .4965 (d) P(−2.70 ≤ Z ≤ 2.70) .9931 (e) P(Z ≤ 1.62) .9474 (f) P(−1.55 ≤ Z) .9394 (g) P(−1.70 ≤ Z ≤ 2.00) .9327 (h) P(1.62 ≤ Z ≤ 2.50) .0464 (i) P(1.70 ≤ Z) .0445 (j) P(|Z| ≤ 2.50) .9876

Answer 1

Answer:

A standard normal distribution refers to a normal distribution with a mean of 0 and a standard deviation of 1. To solve this proble we're going to need the help of a calculator:

(a) P(0 ≤ Z ≤ 2.38) = 0.4913

(b) P(0 ≤ Z ≤ 1) = 0.3413

(c) P(−2.70 ≤ Z ≤ 0) = 0.4965

(d) P(−2.70 ≤ Z ≤ 2.70) = 0.9931

(e) P(Z ≤ 1.62) = 0.9474

(f) P(−1.55 ≤ Z)= 0.9394

(g) P(−1.70 ≤ Z ≤ 2.00) = 0.9327

(h) P(1.62 ≤ Z ≤ 2.50) = 0.0464

(i) P(1.70 ≤ Z) = 0.0445

(j) P(|Z| ≤ 2.50) = 0.9876

All values are verified! ✅