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.)

Answers

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

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