STAT 200 Final Exam (FALL 2016) STAT 200 Final Exam 2016 | Page 7

13. Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean
of 500 and a standard deviation of 100. Show all work.
(a) Consider all random samples of 64 test scores. What is the standard deviation of the
sample
means?
(b) What is the probability that 64 randomly selected test scores will have a mean test score
that is between 475 and 525?
14. An insurance company checks police records on 1200 randomly selected auto accidents
and notes that teenagers were at the wheel in 180 of them. Construct a 90% confidence
interval
estimate of the proportion of auto accidents that involve teenage drivers. Show all work.
15. A city built a new parking garage in a business district. For a random sample of 64 days,
daily fees collected averaged $2,000, with a standard deviation of $400. Construct a 95%
confidence interval estimate of the mean daily income this parking garage generates. Show
all work.
16. ABC Company claims that the proportion of its employees investing in individual
investment
accounts is higher than national proportion of 45%. A survey of 100 employees in ABC
Company indicated that 50 of them have invested in an individual investment account.
Assume Mimi wants to use a 0.10 significance level to test the claim.
(a) Identify the null hypothesis and the alternative hypothesis.