Question

We know that the population distribution for the number of hours that Americans sleep per night is normally distributed with a mean of 6.7 and a standard deviation of 1.4. a) What is the probability that a single, randomly draw observation (i.e., American) from this distribution sleeps less than 5 hours per night? b) What is the probability that a randomly drawn observation falls between 6 and 8 hours per night? c) What is the probability that a randomly draw observation is less than 7 hours per night?

Answer 1

We are given the distribution here as:

a) The probability the the sleep is less than 5 hours is computed here as:
P(X < 5)

converting it to a standard normal variable, we get here:

Getting from the standard normal tables, we get here:

Therefore 0.1123 is the required probability here.

b) Probability that a randomly drawn observation falls between 6 and 8 hours per night is computed here as:
P(6 < X < 8)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.5149 is the required probability here.

c) Now the probability that a randomly draw observation is less than 7 hours per night is computed here as:

P(X < 7)

Converting it to a standard normal tables, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.5848 is the required probability here.