hw normal Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the quest 1) 1) If a particular set of data is approximately normally distributed, we would find that approximately 1 standard deviation around the mean. A) 2 of every 3 observations would fall between B) 19 of every 20 observations would fall between 2 standard deviations around the mean. C) 4 of every 5 observations would fall between 1.28 standard deviations around the mean. D) All the above. 2) The 2) For some value of Z, the value of the cumulative standardized normal distribution is 0.2090. value of Z is A) -0.81 B) 1.96 C) 0.31 D) -0.31 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question 3) A food processor packages orange juice in small jars. The weights of the filled jars3)are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounce. Find the proportion of all jars packaged by this process that have weights that fall below 10.875 ounces. 4) 4) A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. What proportion of the plan recipients would receive payments beyond age 75? 5) 5) The amount of tea leaves in a can from a particular production line is normally distributed with = 110 grams and= 25 grams. a)What is the probability that a randomly selected can will contain between 100 and 120 grams of tea leaves? b) 80% of the cams contain how many leaves? 6) 6) You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, = sdv 9.5. What is the probability of a score between 90 and 95? What is th score for the low 6% of data? SCENARIO 6-2 John has two jobs. For daytime work at a jewelry store he is paid $5,000 per month, plus a commission. His monthly commission is normally distributed with mean $6,000 and standard deviation $1,000. At night he works as a waiter, which his monthly income is normally distributed with mean $1,000 and standard deviation $300. John's income lev from these two sources are independent of each other. 7) Referring to Scenario 6-2, for a given month, what is the probability that John's 7) commission from the jewelry store is less than $13,000? 8) salary 8) Referring to Scenario 6-2, for a given month, what is the probability that John's total is between $28000 and $14,000? 1