Let the random variable Z follow a standard normal distribution. a. Find P1Z 6 1.202.b. Find P1Z 7 1.332.c. Find P1Z 7-1.702.d. Find P1Z 7-1.002.e. Find P11.20 6 Z 6 1.332.f. Find P1-1.70 6 Z 6 1.202.g. Find P1-1.70 6 Z 6-1.002.

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).

(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

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