Question

2. According to survey data collected from 500 students in a recent Statistics class, the histogram for the number of hours of sleep they typically got per night is close to the normal curve with an average of 6.5 hours and a SD of 1.4 hours.

a) Find percentage of students who sleep between 7 and 8 hours

b) A student who sleeps 7 hours per night is at the _______th percentile of the score distribution

c) Find the first quartile of the sleep time and explain your result.

Answer 1

2)

a)

Let X denote the number of hours of sleep they typically got per night.

Since distribution is approximately normal. Then

Required percentage = 21.711%

b)

Now,

So, the student is at 64.058th percentile.

c)

Let 'x' be the first quartile. Then

So, 25% of students sleep less than of equal to 5.5557 hours.