Solution Found!
The random variable x has a normal distribution with ? =
Chapter 4, Problem 92E(choose chapter or problem)
Problem 92E
The random variable x has a normal distribution with μ = 1,000 and σ = 10.
a. Find the probability that x assumes a value more than 2 standard deviations from its mean. More than 3 standard deviations from μ.
b. Find the probability that x assumes a value within 1 standard deviation of its mean. Within 2 standard deviations of μ.
c. Find the value of x that represents the 80th percentile of this distribution. The 10th percentile.
Questions & Answers
QUESTION:
Problem 92E
The random variable x has a normal distribution with μ = 1,000 and σ = 10.
a. Find the probability that x assumes a value more than 2 standard deviations from its mean. More than 3 standard deviations from μ.
b. Find the probability that x assumes a value within 1 standard deviation of its mean. Within 2 standard deviations of μ.
c. Find the value of x that represents the 80th percentile of this distribution. The 10th percentile.
ANSWER:
Step 1 of 7
Let X follows a normal distribution with mean, 
a)
The probability that x assumes a value more than 2 standard deviations from its mean is defined as:
Hence, the required probability is: 