Question

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)

1. To the given question probability is 0.6847 to four decimal places.
What is probability?
• Probability refers to potential. A random event’s occurrence is the subject of this area of mathematics.
• The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
• The degree to something which is likely to happen is basically what probability means. You will understand the potential consequences for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.
• Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
Here, we’ll want to use z scoring to determine the probabilities that x will be either 9 or 5, after which we’ll subtract P(x=5) from P(x=9) to determine the likelihood that x will fall between these two numbers.
Find the z score for every value to begin.
x = 9 , z = (x-μ)/σ = (9-6)/2 = 3/2
x = 5 , z = (x-μ)/σ = (5-6)/2 = -1/2
The probability for every individual z score can then be determined using the z score table.
P(x<=5) = .3085
P(x<=9)= .9332
Subtract P(x=9) from P(x=5) to get.9932 -.3085, which equals .6847