Aset of exam scores is normally distributed and has a mean of 74.4 and a standard deviation of 8.5. what is the probability that a randomly selected score will be between 69 and 77?

answer = (round to four decimal places)

note: be use the z table not use technology or the 68-95-99.7 rule.

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".    

Let X the random variable who represent the exam scores for the population, and for this case we know the distribution for X is given by:  

Where and  

And let represent the sample mean, the distribution for the sample mean is given by:  

What is the probability that a randomly selected score will be between 69 and 77?

For this case we can use the z score formula given by:

And that correspond with the 35.75% of the data.

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