Question

The time a student sleeps per night has a distribution with mean 6.3 hours and a standard deviation of 0.6 hours. Find the probability that average sleeping time for a randomly selected sample of 42 students is more than 6.5 hours per night. Answer: (round to 4 decimal places)

Answer 1

Given,

= 6.3

= 0.6

n =42

Now calculate p(x > 6.5)

p(x > 6.5) = 0.5 - p(0< z < x-/(/n) ​​​​​​)

= 0.5 - p(0 < z < 6.5-6.3/(0.6/42))

= 0.5 - p(0 < z < 2.16)

= 0.5 - 0.4846

P(x > 6.5) = 0.0154

Therefore the probability that mean is more than 6.5 hours per night is 0.0154.