University and college students average 7.2 hours of sleep per night, with a standard deviation of 40 minutes. find the amount of sleep that is exceeded by only 25% of students.

The answer is 7.65 hours.

Since only 25% of college students exceed this amount, this means that 75% of college students sleep less than this.  We look this value up in a z-table (http://www.z-table.com) and see that the z-score with this probability is closer to 0.67.  

Before we use the formula for a z-score, we must convert 7.2 hours to minutes:
7.2(60) = 432

Using the formula for a z-score:
z = (X-μ)/σ
0.67 = (x-432)/40

Multiply both sides by 40:
0.67(40) = ((x-432)/40)*40
26.8 = x-432

Add 432 to both sides:
26.8+432 = x-432+432
458.8 = x

Divide by 60 to convert to hours:
458.8/60 = 7.65

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