Question

In example 5.1, the total sleep time per night among college students was approximately normally distributed with mean µ = 6.78 hours and standard deviation s = 1.24 hours. suppose you plan to take an srs of size n = 150 and compute the average total sleep time. what is the probability that your average will be below 6.9 hours?what is the probability that your average will be below 6.9 hours? ( fill in the blank below and round your answer to 4 decimal places.) ( fill in the blank below and round your answer to 4 decimal places.)

Answer 1

first we calculate the standard deviation for the average time whose formula is 
σ / $\sqrt{n}$
= 1.24 / $\sqrt{150}$
= 0.1012

the probability that the average is below 6.9 hours
P(z= [6.9-6.78] / 0.1012)
= P(z= 1.1858)

use the standard normal distribution table to find z
the probability will thus be 0.8810