Consider a normally distributed population with a mean =173=173 and standard deviation =62=62. Suppose random samples of size n=10=10 are selected from this population.

1. a) What is the mean of the distribution of the sample mean? x== b) What is the standard error of the mean? (2 decimal places) x==
2. What is the probability that a randomly selected sample mean is: a) greater than 168.1? b) less than 177.1? c) greater than 168.1 and less than 177.1?
3. Between what values would you expect to find the middle 86% of the sample means? Round to the nearest integer. Between and .
4. Why are we able to use the normal distribution in the calculations above?
   • Because the original population is normal
   • Because the sample size is large enough
   • Because the sample mean is large enough
   • Becasuse the standard error is large enough