Question

Another researcher found that the hours of sleep for female students is normally distributed with a mean of 8 hours and a standard deviation of 25.81 minutes.

1. (1 mark) What is the probability that a randomly selected female student at the college sleep less than 8.12 hours? (4dp)  Answer

2. What is the probability that a randomly selected female student at the college sleep more than 7.98 hours? (4dp)  Answer

3. What is the probability that a randomly selected female student at the college sleeps between 7.88 and 8.36 hours? (4dp)  Answer

4. (1 mark) If the hours of sleep for a female student was on the 66th percentile, how many hours would she be sleeping? (2dp)  Answer hours

5. In a sample of 33 female students, how many of them would be expected to sleep more than 7.98 hours? (2 dp)  Answer

Answer 1

a)

b)

c)

d)

Given that 66th percentile

Z score for 66th percentile is 0.4124

X = μ + Z * σ

= 8 + 25.81 *0.4124

= 8 + 10.64

= 18.64

e)

Given that sample n = 33

Probability of students sleep more than 7.98 hours

P( X > 7.98 ) = P( Z > 7.98 - 8 / 25.81 / Sqrt(33))

= P( Z > 0.02 / 4.493 )

=P( Z > 0.0044 )

Using standard normal table

P( Z > 0.0044 ) = 0.5