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A statistics analysis of a sample of actors and actresses in los angeles. The analysis includes their salaries, the prevalence of plastic surgery and fear of aliens, and their preferred dog weights. The document also includes calculations of mean, median, standard deviation, interquartile range, and probabilities.
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ECON 230 Test 1 Name: Section (Circle one): 9:25 10: You will be graded based on the answers that you write below. Please make sure to include all of your work on the sheets provided. Part 1:
Mean
ii) Standard deviation =
iii) A. The 50th^ percentile also happens somewhere in the first class, and 3 lbs is the only choice in the first class. iv) Lower end = 4.5 – 23.22 = -1. Upper end = 4.5 + 23.22 = 10.
ii) Here you wanted to use the complement rule: If it’s not the case that at least one actor prefers a dog that weighs more than 5 pounds, then it is the case that no actors prefer their dog to weigh more than 5 pounds. So: P(no actors are Y) + P(at least one is Y) = 1 P(at least one is Y) = 1 - P(no actors are Y) P(no actors are Y) = P(NNN) =
So: P(at least one is Y) = 1 – 0.508 = 0. iii) We know that: P(0 actors are Y) + P(1 actor is Y) + P(2 actors are Y) + P(3 actors are Y) = 1
Part 1: You are an enterprising reporter for the Weekly World News. You hope to learn about the lives of actors and actresses. Your boss at the Weekly World News gives you a list of the phone numbers of all actors and actresses who live in Los Angeles. You pick five names at random from the list and call them up.
iv) What is the interquartile range? v) Suppose that the highest salary in the sample went up. A) only the mean would change B) the mean and mode would both change C) the mean and the median would change D) the mean, the median, and the mode would all change. vi) Suppose that you called up a sixth person and discovered that the mean salary of the six actors in your sample was 1750. What is the sixth actor’s salary?
Part 2
iv) The probability that exactly one actor prefers dogs that weigh more than 5 pounds. Extra credit: Calculate the standard deviation of the data in the table from part 4. Use the mean that you calculated in part 4) and this standard deviation, together with Chebyshev’s Theorem to find an interval that must contain 84% of the data. (3 points)