Question

Salaries for teachers in a particular elementary school district are normally distributed with a mean of $44,000 and a
standard deviation of $6,500. We randomly survey ten teachers from that district.
1.Find the probability that the teachers earn a total of over $400,000

2.If we surveyed 70 teachers instead of ten, graphically, how would that change the distribution in part d?

3.If each of the 70 teachers received a $3,000 raise, graphically, how would that change the distribution in part b?

Answer 1

1.0.0262

2. Probability increases as sample size increases. So sampling 70 teachers instead of ten would cause the distribution to be more spread out. It would be a more symmetrical normal curve.

3. If every teacher received a $3,000 raise, the distribution of X would shift to the right by $3,000. In other words, it would have a mean of $47,000.