Find the following probability for the standard normal random variable z. a. P(z= 2) e. P(-2szs2) f. P(-3szs3) g. P(- 2.99 2) a. P(z= 2) = (Round to three decimal places as needed.)
Find the following probability for the standard normal random variable z. a. P(z= 2) e. P(-2szs2) f. P(-3szs3) g. P(- 2.99 2) a. P(z= 2) = (Round to three decimal places as needed.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 22E
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![### Standard Normal Distribution Probabilities
Find the following probabilities for the standard normal random variable \( z \):
a. \( P(z = 2) \)
b. \( P(z \leq 2) \)
c. \( P(z < 2) \)
d. \( P(z > 2) \)
e. \( P(-2 \leq z \leq 2) \)
f. \( P(-3 \leq z \leq 3) \)
g. \( P(-2.99 \leq z \leq 0.51) \)
h. \( P(-0.61 < z < 1.06) \)
#### Example Calculation
a. \( P(z = 2) = \) [Input your answer, rounded to three decimal places as needed.]
This set of problems requires finding probabilities related to the standard normal distribution, which is typically represented as \( N(0,1) \). Remember to use the standard normal distribution table or a calculator for precise values, especially when rounding to three decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40766f6b-1d39-4de4-8cc4-4220165d991f%2F02838c54-025f-414f-b490-14b98c94e308%2Ftrkfm7r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Standard Normal Distribution Probabilities
Find the following probabilities for the standard normal random variable \( z \):
a. \( P(z = 2) \)
b. \( P(z \leq 2) \)
c. \( P(z < 2) \)
d. \( P(z > 2) \)
e. \( P(-2 \leq z \leq 2) \)
f. \( P(-3 \leq z \leq 3) \)
g. \( P(-2.99 \leq z \leq 0.51) \)
h. \( P(-0.61 < z < 1.06) \)
#### Example Calculation
a. \( P(z = 2) = \) [Input your answer, rounded to three decimal places as needed.]
This set of problems requires finding probabilities related to the standard normal distribution, which is typically represented as \( N(0,1) \). Remember to use the standard normal distribution table or a calculator for precise values, especially when rounding to three decimal places.
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