Question

Play around and calculate a few values:

a) Φ(0) = ?
b) Φ(1) = ?
c) Φ(0) = ?
d) P(−1 < Z < 1) = Φ(1) − Φ (−1) = ?
e) P(−2f) P(−1.96

Answer 1

To calculate the values, we need to use the concepts of Φ and P in probability. The values are calculated as follows: a) Φ(0) = 0.5, b) Φ(1) = 0.8413, c) Φ(0) = 0.5, d) P(-1 < Z < 1) = 0.6826, and e) P(-2 < Z < 1.96) = 0.9522.

Step-by-step explanation:

To calculate the values, we need to understand the concepts of Φ and P in probability.

a) Φ(0) = 0.5, because the standard normal distribution is symmetrical and the area to the left and right of 0 is equal.

b) Φ(1) = 0.8413, which means that the area to the left of 1 in the standard normal distribution is 0.8413.

c) Φ(0) = 0.5, as mentioned in part a.

d) P(-1 < Z < 1) = Φ(1) - Φ(-1) = 0.8413 - 0.1587 = 0.6826.

e) P(-2 < Z < 1.96) = Φ(1.96) - Φ(-2) = 0.9750 - 0.0228 = 0.9522.