Question

Given that z is a standard normal random variable, compute the following probabilities (to 4 decimals).

1. P(-1.93 ≤ z ≤ 0.44)
   
   
2. P(0.59 ≤ z ≤ 1.27)
   
   
3. P(-1.74 ≤ z ≤ -1.05)

Answer 1

1. P( -1.93 ≤ z ≤ 0.44) = P( z ≤ 0.44) – P(z ≤ -1.93)

Using standard normal distribution table, P( z ≤ 0.44) = 0.6700, P(z ≤ -1.93) = 0.0268

P( -1.93 ≤ z ≤ 0.44) = 0.6700 – 0.0268 = 0.6432

P( -1.93 ≤ z ≤ 0.44) = 0.6432

2. P( 0.59 ≤ z ≤ 1.27) = P( z ≤ 1.27) – P(z ≤ 0.59)

Using standard normal distribution table, P( z ≤ 1.27) = 0.8980, P(z ≤ 0.59) = 0.7224

P( 0.59 ≤ z ≤ 1.27) = 0.8980 – 0.7224 = 0.1756

P(0.59 ≤ z ≤ 1.27) = 0.1756

3. P(-1.74 ≤ z ≤ -1.05) = P( z ≤ -1.05) – P(z ≤ -1.74)

Using standard normal distribution table, P( z ≤ -1.74) = 0.0409, P(z ≤ -1.05) = 0.1469

P(-1.74 ≤ z ≤ -1.05) = 0.1469 - 0.0409 = 0.1059

P(-1.74 ≤ z ≤ -1.05) = 0.1059