Math 140 Statistics Chapter 5 Homework Questions Answer all questions and submit your ALL your work shown (formulas). 1. Avariable Y of a finite population has the following frequency distribution: Y O 1 3 6 Frequency 18 14 8 1O a) Determine the probability distribution of Y. b) Find the probability of P( Y = 3). c) Interpret the P(Y=3). d) Construct a probability histogram for Y. Determine whether a probability distribution is given in questions #2 and 3. In those cases where a probability distribution is not described (not satised), identify why it is not satisfied. In those cases where the probability distribution is satisfied, find the mean and standard deviation. 2. The Baltimore Computer House reports that the probabilities of selling 0,J_,2,,and_4 microcomputers in one day are: .240,.370, .205, .075 and .080 respectively. 3. The number of dinners that typical Americans cook in a week are listed with their probabilities (from USA Today): X Probability .08 .05 .21 .09 4. Choose a young person (ages 19-25) at random and ask \"In the past seven days, how many days did you watch television?\" The discrete random variable is X = the number of days you watched television. X 0 1 2 Probability .04 .03 .06 .08 .09 .08 .05 ??? a) What is the probability of P(X=7)? b) Calculate the mean and standard deviation for the number of days watching television. Y Probability 0.36 0.28 0.16 0.20 a) Find the mean of the discrete random variable Y. b) Find the standard deviation of discrete random variable Y. 6. Sophia was recently promoted to assistant manager at a small women's clothing store. One of her duties is to fill out order forms for women's shirts, which come in sizes 6,7,8,9,10,11, and 12. She would like to determine how many shirts of each size to order. At rst, she thought of ordering exactly the same number of shirts from each of the available sizes, but then she decided against doing that, because there might be demand for certain sizes. She looked up sales receipts from the past three months and summarized the information below: Shirt Size 6 7 8 9 10 11 12 Number 85 122 138 154 177 133 92 Sold a) Create a probability distribution for the above data. b) What is the probability of selecting a size 11 shirt? c) What is the probability of selecting at least a size 11 shirt? d) Compute the mean and standard deviation of shirt size. e) If Sophia plans to order 1,000 shirts, how many of size 8 should she order? 7. Space Shuttles. The random variable X is the crew size of a randomly selected shuttle mission between April 12, 1981 and July 8, 2011. The probabilty distribution is in the table below. X 2 4 5 6 7 8 Probability 0.030 0.022 0.267 0.207 0.467 0.007 a) What do you estimate the mean of the variable will be? b) Find and interpret the mean of the random variable c) How was your estimate? 8. Homeowners Policy. An insurance company wants to design a homeowner's policy for mis-priced homes. From data compiled by the company it is known that the annual claim in thousands of dollars per homeowner is a random variable with the following probability distribution: X 0 10 50 100 200 Probability 0.95 0.045 0.004 0.0009 0.0001 a) Determine the mean (expected value) annual claim amount per homeowner. b) How much should the insurance company charge for the annual premium if they want to have an average net profit of $50? 9. For each of the following probability histogram of biqnqmiaj distributions specify whether the success probability is less than, equal to of greater than .5. Explain your answer. Probability for X 0.3 Probability for X 0_3 0.23 0.2 0.2 0.1 - - I - - 0 0 D 1 2 3 4 0 1 2 3 4 5 a) b) 10. Carbon Tax. A poll commissioned by the Friends of the Earth and conducted by the Mellman Group found that 72% of American voters are in favor of the carbon tax. Suppose six voters are randomly sampled and asked if they favor a carbon tax. Determine the probability that the number answering Yes is: a) Exactly two b) Exactly four c) At least four d) What shape will the histogram be