Final exam scores are normally distributed with a mean of 74 and a standard deviation of 6. approximately, what percentage of final exam scores would be between 68 and 86?

81.86%

Step-by-step explanation:

We have been given that final exam scores are normally distributed with a mean of 74 and a standard deviation of 6.

First of all we will find z-score using z-score formula.

Now let us find z-score for 86.

Now we will find P(-1<Z) which is probability that a random score would be greater than 68. We will find P(2>Z) which is probability that a random score would be less than 86.

Using normal distribution table we will get,    

We will use formula to find the probability to find that a normal variable lies between two values.

Upon substituting our given values in above formula we will get,

Upon converting 0.81859 to percentage we will get

Therefore, 81.86% of final exam score will be between 68 and 86.  

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