Question

pdf 0.15 0.20 0.10 0.15 0.40 Tip amount $4 S8 $15 S22 Use the following information to answer questions 3 – 6: Suppose that waiters' tips across all customers and restaurants in California are distributed according to the pdf pictured above the blue numbers represent areas within the intervals in which they are pictured). 3. What is the median tip amount? (Don't enter a dollar sign as part of your answer) (If the answer cannot be determined without more information, enter 99 as your answer) 4. What is the probability that a waiter will receive a tip between $4 and $15? (If you think the answer is 23%, write 23 for your answer. Do NOT write 0.23 and do NOT write 23%). 5. This distribution is skewed right. As such, what is the most you can say about the expected value of this distribution, given the information in this pdf? a. The expected value is above $22. b. The expected value is above $15. c. The expected value is below $15. d. Knowing the range in which the expected value is located is impossible without more information. 6. What is the height of the CDF for this distribution at a horizontal value of $22? (Your answer will be between 0 and 1, so – for example – it might be 0.30, but it could not be 30).

Answer 1

3) The median will be the amount which is more than 50% of the numbers. So, here median amount would be 15, as the cumulative probability till $15 is 0.15+0.15+0.2 = 0.5.

4) Probability that a waiter will receive a tip between $4 and $15 = 0.15 + 0.20 = 0.35

5) As the distribution is skewed right , the mean of the distribution will be greater than the median. As the median is $15, the expected value would be above $15. So, option b is the correct answer.

6) The CDF for this distribution at a horizontal value of $22 will be 0.15 + 0.15 + 0.20 + 0.40 = 0.90.

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