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Consider a normal distribution with mean 35 and standard deviation 4. What is the probability a value selected at random from this distribution is greater than 35? (Round your answer to two decimal places.)



Answer :

Given the Mean:

[tex]\mu=35[/tex]

And the Standard Deviation:

[tex]\sigma=4[/tex]

You need to find:

[tex]P(X>35)[/tex]

You can find the z-statistics using this formula:

[tex]z=\frac{X-\mu}{\sigma}[/tex]

In this case, you need to set up that:

[tex]X=35[/tex]

Then, substituting values and evaluating, you get:

[tex]z=\frac{35-35}{4}=0[/tex]

Therefore, you need to find:

[tex]P(z>0)[/tex]

Using the Normal Distribution Table for that z-statistic, you get:

[tex]P(z>0)=0.50[/tex]

Hence, the answer is:

[tex]P(X>35)=0.50[/tex]

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