Assume the random variable X is normally distributed with mean

mu equals 50μ=50

and standard deviation

sigma equals 7σ=7.

Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded.

Upper P left parenthesis 34 less than Upper X less than 63 right parenthesis

P(34

And we can find this probability with this difference and using the normal standard table or excel:

And the result is illustrated in the figure attached.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

Where and

We are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

If we apply this formula to our probability we got this:

And we can find this probability with this difference and using the normal standard table or excel:

And the result is illustrated in the figure attached.

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