Supposed we have a population that is normally distributed with a mean= 106, and a standard deviation= 12.

a. What is the probabilityof selecting a single observation that is less than 100?

b. If a sample of N=25 is taken, what is the probability that the meanof the sample exceeds 12?

c. Find the probability that the sample mean of a sample of N= 16 will not differ from the population mean of 106 by more than +/-6 units.

Supposed we have a population that is normally distributed with a mean= 106, and a standard deviation= 12.

a. What is the probability of selecting a single observation that is less than 100?

Solution: Let X be a random variable following a normal distribution with mean=106 and standard deviation =12. Then X~N(106, 12^2). So, Z=(X-106)/12~N(0,1), the standard normal distribution.

So, the probability …

The solution determines what is the probability of selecting a single observation that is less than 100.