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.

Question

Computers & Technology

Quinn Adams

11 July, 21:05

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.

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Answers (1)

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Angela Gordon · Answer 1

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
(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).

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).

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