The data in the question seems a bit erroneous so I am writing the complete question below:
Let the random variable Z follow a standard normal distribution.
a. Find P(Z < 1.20).
b. Find P(Z > 1.33).
c. Find P(Z > -1.70).
d. Find P(Z > -1.00).
e. Find P(1.20 < Z < 1.33).
f. Find P(-1.70 < Z < 1.20).
g. Find P(-1.70 < Z < -1.00).
Answer:
(a) P(Z < 1.20) = 0.8849
(b) P(Z > 1.33) = 0.0918
(c) P(Z > -1.70) = 0.9554
(d) P(Z > -1.00) = 0.8413
(e) P(1.20 < Z < 1.33) = 0.0233
(f) P(-1.70 < Z < 1.20) = 0.8403
(g) P(-1.70 < Z < -1.00) = 0.1141
Explanation:
To answer this question, we would need to use the Normal Distribution Probability table. The table shows areas under the normal curve to the left of the z value i.e. it shows P(Z<x).
(a) We need to compute P(Z < 1.20). For this, we will look for the area under the normal curve at z=1.20 in the Normal Distribution Probability Table. So,
P(Z < 1.20) = 0.8849
(b) Now we need to compute P(Z > 1.33). For this, we will find the value of P(Z<1.33) from the normal probability table and subtract it from 1 to get P(Z > 1.33).
P(Z > 1.33) = 1 - P(Z < 1.33)
= 1 - 0.9082
P(Z > 1.33) = 0.0918
(c) Similar to part (b), we will find the value of P(Z<-1.70) by looking at the area under the normal curve at Z = -1.70 and then subtract it from 1 to find P(Z > -1.70).
P(Z > -1.70) = 1 - P(Z < -1.70)
= 1 - 0.0446
P(Z > -1.70) = 0.9554
(d) P(Z > -1.00) = 1 - P(Z < -1.00)
= 1 - 0.1587
P(Z > -1.00) = 0.8413
(e) To compute P(1.20 < Z < 1.33), we will first find the value of P(Z<1.20) and subtract it from the value of P(Z<1.33) using the normal distribution table.
P(1.20 < Z < 1.33) = P(Z < 1.33) - P(Z < 1.20)
= 0.9082 - 0.8849
P(1.20 < Z < 1.33) = 0.0233
(f) P(-1.70 < Z < 1.20) = P(Z < 1.20) - P(Z < -1.70)
= 0.8849 - 0.0446
P(-1.70 < Z < 1.20) = 0.8403
(g) P(-1.70 < Z < -1.00) = P(Z < -1.00) - P(Z < -1.70)
= 0.1587 - 0.0446
P(-1.70 < Z < -1.00) = 0.1141
