1. Let random variable x represent the number of heads when a fair coin is tossed two times.
(a) Construct a table describing the probability distribution.
(b) Determine the mean and standard deviation of x. (Round the answer to two decimal places)
2. Mimi plans on growing tomatoes in her garden. She has 20 cherry tomato seeds. Based on her experience, the probability of a seed turning into a seedling is 0.60.
(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.
3. 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)
4. 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?
5. 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.
6. 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% confidence interval estimate of the mean daily income this parking garage generates. Show all work. Just the answer, without supporting work, will receive no credit.
7. A researcher claims the proportion of auto accidents that involve teenage drivers is less than 20%. ABC Insurance Company checks police records on 200 randomly selected auto accidents and notes that teenagers were at the wheel in 32 of them.
Assume the company wants to use a 0.05 significance level to test the researcher's claim.
(a) Identify the null hypothesis and the alternative hypothesis.
(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
(c) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.
(d) Is there sufficient evidence to support the researcher's claim that the proportion of auto accidents that involve teenage drivers is less than 20%? Explain.