STAT 200 FINAL EXAMINATION, SPRING 2017 STAT 200 FINAL EXAMINATION, | Page 5

(a) Let X be the number of seedlings that Mimi gets. As we know, the distribution of X is a
binomial probability distribution. What is the number of trials (n), probability of successes (p) and
probability of failures (q), respectively?
(b) Find the probability that she gets at least 15 cherry tomato seedlings. (round the answer to 3
decimal places) ​ Show all work. Just the answer, without supporting work, will receive no credit
11. ​ The heights of pecan trees are normally distributed with a mean of 10 feet and a standard
deviation of 2 feet. ​ Show all work. Just the answer, without supporting work, will receive no
credit.
(a) What is the probability that a randomly selected pecan tree is between 9 and 12 feet tall?
(round the answer to 4 decimal places)
(b) Find the 80th percentile of the pecan tree height distribution. (round the answer to 2 decimal
places)
12. ​ Based on the performance of all individuals who tested between July 1, 2012 and June 30,
2015, the GRE Quantitative Reasoning scores are normally distributed with a mean of 152.47
and a standard deviation of 8.93. (https://www.ets.org/s/gre/pdf/gre_guide_table1a.pdf). ​ Show
all work. Just the answer, without supporting work, will receive no credit.
(a) Consider all random samples of 36 test scores. What is the standard deviation of the sample
means? (Round your answer to three decimal places)
(b) What is the probability that 36 randomly selected test scores will have a mean test score that
is between 148 and 152?
13. ​ A survey showed that 1200 of the 1600 adult respondents believe in global warming.
Construct a 95% confidence interval estimate of the proportion of adults believing in global
warming. ​ Show all work. Just the answer, without supporting work, will receive no credit.
14. ​ A city built a new parking garage in a business district. For a random sample of 100 days,
daily fees collected averaged $2,000, with a standard deviation of $500. Construct a 90%