This question is similar to Exercises 10-16 on pages 287-288 of your textbook. Let z be the standard normal variable and x be a normal random variable with the mean μ = 15 and the standard deviation o = 8. Find the following probabilities and the value of a. a. P(Z < 0.58). b. P(z > -1.24),
This question is similar to Exercises 10-16 on pages 287-288 of your textbook. Let z be the standard normal variable and x be a normal random variable with the mean μ = 15 and the standard deviation o = 8. Find the following probabilities and the value of a. a. P(Z < 0.58). b. P(z > -1.24),
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:This question is similar to Exercises 10–16 on pages 287–288 of your textbook.
Let \( z \) be the standard normal variable and \( x \) be a normal random variable with the mean \( \mu = 15 \) and the standard deviation \( \sigma = 8 \). Find the following probabilities and the value of \( a \).
a. \( P(z < 0.58) \).
b. \( P(z > -1.24) \).
c. \( P(x \geq a) = 0.85 \).

Transcribed Image Text:The text appears to be a set of probability and statistics exercises involving the computation and interpretation of probabilities. Below is the transcribed content suitable for an educational website:
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**Probability Exercises:**
d. \( P(1.06 < z < 2.73) \).
e. \( P(z > a) = 0.74 \). Find \( a \).
f. Find \( P(x < 21) \).
g. Find \( P(x > 13) \).
h. Find \( P(5 < x < 26.6) \).
i. Find \( P(20 < x < 27) \).
j. \( P(x < a) = 0.92 \). Find \( a \).
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These exercises involve understanding the properties of probability distributions, calculating probabilities for given conditions, and determining unknown variables with probability constraints.
Expert Solution

Step 1
Given that.
X~N( μ , ?)
μ=15 , ?=8
Z-score =( x - μ )/?
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