A population of values has a normal distribution with u 57.3 and o = 37.8. a. Find the probability that a single randomly selected value is less than 50.8. Round your answer to four decimal places. P(X < 50.8) = -0.3413 108 has a mean less than 50.8. b. Find the probability that a randomly selected sample of size n = Round your answer to four decimal places. P(M < 50.8) =
A population of values has a normal distribution with u 57.3 and o = 37.8. a. Find the probability that a single randomly selected value is less than 50.8. Round your answer to four decimal places. P(X < 50.8) = -0.3413 108 has a mean less than 50.8. b. Find the probability that a randomly selected sample of size n = Round your answer to four decimal places. P(M < 50.8) =
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![**Normal Distribution Analysis**
A population of values follows a normal distribution characterized by:
- Mean (\(\mu\)) = 57.3
- Standard deviation (\(\sigma\)) = 37.8
**Tasks:**
a. **Probability of a Single Value**
Determine the probability that a single randomly selected value is less than 50.8. Ensure that your answer is rounded to four decimal places:
\[
P(X < 50.8) = \boxed{-0.3413}
\]
b. **Probability of a Sample Mean**
Determine the probability that the mean of a randomly selected sample of size \( n = 108 \) is less than 50.8. Ensure that your answer is rounded to four decimal places:
\[
P(M < 50.8) = \boxed{\phantom{-} }
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4cbdcd8-71de-429b-b001-27d54b327ca5%2F4fb40e1e-eddd-43a4-8c6a-a42c8ebe4f27%2Fpdh8pad_processed.png&w=3840&q=75)
Transcribed Image Text:**Normal Distribution Analysis**
A population of values follows a normal distribution characterized by:
- Mean (\(\mu\)) = 57.3
- Standard deviation (\(\sigma\)) = 37.8
**Tasks:**
a. **Probability of a Single Value**
Determine the probability that a single randomly selected value is less than 50.8. Ensure that your answer is rounded to four decimal places:
\[
P(X < 50.8) = \boxed{-0.3413}
\]
b. **Probability of a Sample Mean**
Determine the probability that the mean of a randomly selected sample of size \( n = 108 \) is less than 50.8. Ensure that your answer is rounded to four decimal places:
\[
P(M < 50.8) = \boxed{\phantom{-} }
\]
Expert Solution
Step 1
We have given that
X~N( μ , ?^2 )
μ =57.3 , ? = 37.8
Z-score =( x - μ )/?
n=108
Step by step
Solved in 2 steps with 1 images
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