Find the following probability for the standard normal random variable z. e. P(z 20) f. P(-2.54 szs1.35) g. P(z> - 2.15) h. P(z< 2.15) a. P(z>1.15) b. P(z< - 1.83) c. P(0.01szs2.63) d. P(-1.981.15) = .125 (Round to three decimal places as needed.) b. P(z< -1.83) = .034 (Round to three decimal places as needed.) c. P(0.01szs2.63) = .492 (Round to three decimal places as needed.) d. P(-1.98 sz< - 0.64) =|(Round to three decimal places as needed.)

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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D through H

**Finding Probabilities for Standard Normal Random Variable Z**

Given the following probabilities for the standard normal random variable \( z \):

a. \( P(z > 1.15) \)

b. \( P(z < -1.83) \)

c. \( P(0.01 \leq z \leq 2.63) \)

d. \( P(-1.98 \leq z < -0.64) \)

e. \( P(z \geq 0) \)

f. \( P(-2.54 \leq z \leq 1.35) \)

g. \( P(z \geq -2.15) \)

h. \( P(z < 2.15) \)

**Calculated Probabilities:**

a. \( P(z > 1.15) = 0.125 \) (Round to three decimal places as needed.)

b. \( P(z < -1.83) = 0.034 \) (Round to three decimal places as needed.)

c. \( P(0.01 \leq z \leq 2.63) = 0.492 \) (Round to three decimal places as needed.)

d. \( P(-1.98 \leq z < -0.64) = \) [Blank, round to three decimal places as needed.]

_Note: Explore statistical tables or software to find the probabilities for any remaining parts._
Transcribed Image Text:**Finding Probabilities for Standard Normal Random Variable Z** Given the following probabilities for the standard normal random variable \( z \): a. \( P(z > 1.15) \) b. \( P(z < -1.83) \) c. \( P(0.01 \leq z \leq 2.63) \) d. \( P(-1.98 \leq z < -0.64) \) e. \( P(z \geq 0) \) f. \( P(-2.54 \leq z \leq 1.35) \) g. \( P(z \geq -2.15) \) h. \( P(z < 2.15) \) **Calculated Probabilities:** a. \( P(z > 1.15) = 0.125 \) (Round to three decimal places as needed.) b. \( P(z < -1.83) = 0.034 \) (Round to three decimal places as needed.) c. \( P(0.01 \leq z \leq 2.63) = 0.492 \) (Round to three decimal places as needed.) d. \( P(-1.98 \leq z < -0.64) = \) [Blank, round to three decimal places as needed.] _Note: Explore statistical tables or software to find the probabilities for any remaining parts._
Expert Solution
Step 1

We have given that 

X~N( 0 , 1)
 
 μ = 0    , ? = 1
 
Z-score =( x - μ )/?
 
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