Answer:
- a) P (Z < - 1.26) = 0.60383
- b) P (Z > 1.48) = 0.56944
- c) P (1.44 < Z < 2.79) = 0.07229
Explanation:
You need to use a table with the cumulative normal standard distribution, which shows the areas for different values of Z-scores.
I attached part of the table for the cumulative probability that gives the probability that a statistic is between 0 (the mean) and Z.
a) P (Z < - 1.26)
The table shows the probabilities for positive values of Z. Since the normal distribution is symmetric P (Z < - 1.26) = P (Z > 1.26).
Also, note that you will find the probability for Z ≤ 1.26, so the probability that you want is P (Z > 1.26) = 1 - P(Z ≤ 1.26)
- From the table: P (Z ≤ 1.26) is 0.39617.
- Then, P (Z > 1.26) = 1 - 0.39617 = 0.60383.
- As said, P (Z < - 1.26) = P (Z > 1.26), so it is 0.60383.
b) P (Z > 1.48)
- P (Z > 1.48) = 1 - P( Z ≤ 1.48)
- From the table, P (Z < 1.48) = 0.43056
- P (Z > 1.48) = 1 - 0.43056 = 0.56944
c) P (1.44 < Z < 2.79)
- P (1.44 < Z < 2.79) = P (Z < 2.79) - P (Z < 1.44)
- From the table: P (Z < 2.79) = 0.49736, and P (Z < 1.44) = 0.42507
- P (Z < 2.79) - P( Z < 1.44) = 0.49736 - 0.42507 = 0.07229
