Answer to Question #169475 in Statistics and Probability for Sunera

Question

Use Cumulative Standardized Normal Probability table to find the following probabilities

a) P( Z ≤ -1.96)

b) P( Z ≤ 2.43)

c) P( Z ≥ 1.7)

d) P( Z ≥ -0.95)

e) P( -2.97 ≤ Z ≤ -1.38)

f) P( -1.14 ≤ Z ≤ 1.55)

Answer 1

All probabilities are being computed with table above. This distribution is symmetrical with respect to y axes, which is the same that P(z ≤ -a) = 1 - P(z ≤ a), a >= 0.

1. 0.025
2. P(z ≤ -2.43) = 0.0075, hence P(z ≤ 2.43) = 1 - 0.0075 = 0.9925
3. P(z ≤ -1.7) = 0.0446. P(z ≥ 1.7) is also equal to 0.0446 because of symmetry
4. P( z ≤ -0.95) = 0.1711. Hence P( z ≥ -0.95) = 1 - 0.1711 = 0.8289
5. P( z ≤ -2.97) = 0.0015, P(z ≤ -1.38) = 0.0838. Hence P( -2.97 ≤ z ≤ -1.38) = 0.0838 - 0.0015 = 0.0823
6. P(z ≤ -1.55) = 0.0606, P(z ≤ 1.55) = 1 - 0.0606 = 0.9394. P(z ≤ -1.14) = 0.1271. Hence P( -1.14 ≤ z ≤ 1.55) = 0.9394 - 0.1271 = 0.8123