The amounts of time students study for an exam follows a normal model with a mean of 6 hours and a standard deviation of 1.5 hours. what is the probability a student studies between 3.5 and 5.5 hours?

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The amounts of time students study for an exam follows a normal model with a mean of 6 hours and a standard deviation of 1.5 hours.

what is the probability a student studies between 3.5 and 5.5 hours?

Expert Solution
Step 1

Obtain the standard z-score for the random variable X equals 3.5.

The standard z-score for the random variable X equals 3.5 is obtained below as follows:

Let X denotes the amounts of time students study for an exam which follows normal distribution with mean of 6 hours and standard deviation of 1.5 hours That is, .

The required standard z-score is,

Statistics homework question answer, step 1, image 1

The standard z-score for the random variable X equals 3.5 is –1.67.

 

Obtain the standard z-score for the random variable X equals 5.5

The standard z-score for the random variable X equals 5.5 is obtained below as follows:

The required standard z-score is,

Statistics homework question answer, step 1, image 2

The standard z-score for the random variable X equals 5.5 is –0.33.

 

 

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