- δΎ‹
- Consider a population with mean = 82 and standard deviation = 12.
- (a)
- If a random sample of size 64 is selected, what is the probability that the sample mean will lie between 80.8 and 83.2?
- (b)
- With a random sample of size 100, what is the probability that the sample mean will lie between 80.8 and 83.2?

- (a)
- We have
and .
Since
*n*=64 is large, the central limit theorem tells us that the distribution of is approximately normal withTo calculate , we convert to the standardized variable

The z-values corresponding to 80.8 and 83.2 are

andConsequently,

- (b)
- We now have
*n*=100, so ,andTherefore,

Note that the interval (80.8, 83.2) is centered at . The probability that will lie in this interval is larger for

*n*=100 than for*n*=64.