In Example 4.4, compute the probability that the test incorrectly identifies the defects D

4.6 Variables: Discrete and Continuous 4.36 Classify each of the following random variables as either continuous or discrete: a. The lifelength of the battery in a smoke alarm b. The number of rain delays during a baseball game played in Seattle during the month of March

c. The thickness of ice 20 feet from the shoreline in Lake Superior during a random day

in December d. The amount of medication prescribed to a patient having high blood pressure e. The speed at which a major league baseball player throws a baseball f. The amount of water spread on a lawn during a random July day in Kansas 4.37 A state consumer bureau is investigating the impact of the state’s new “lemon law” by inspecting new cars on randomly selected car dealerships. The inspectors were looking for defects on the exterior of the cars dents, misfitting doors, uneven painting, etc.. The inspectors record the number of defects per car. Is the number of defects on a randomly selected car a discrete or continuous random variable? Explain your answer. 4.38 The running of red lights by drivers is a serious problem in many cities. A police officer is stationed near a major intersection to observe the traffic for several days.

a. Is the number of cars running a red light during a given light cycle a discrete or

continuous random variable?

b. Is the time between the light turning red and the last car passing through the inter-

section a discrete or continuous random variable? c. Are the brands of cars running a red light a discrete or continuous random variable? 4.39 Every semester, students are given a questionnaire to evaluate their instructor’s teaching. The question that is of greatest interest to administrators is, “Do you agree with the following statement: ‘overall the instructor was a good teacher.’” The possible responses are Strongly agree, Agree, No opinion, Disagree, and Strongly disagree.

a. Are the number of students in class responding Strongly agree a continuous or discrete

random variable?

b. Are the percent of students in class responding Strongly agree a continuous or discrete

random variable? 4.7 Probability Distributions for Discrete Random Variables Bus. 4.40 An appliance store has the following probabilities for y, the number of major appliances sold on a given day: y Py .100 1 .150 2 .250 3 .140 4 .090 5 .080 6 .060 7 .050 8 .040 9 .025 10 .015

a. Construct a graph of Py. b. Find .

c. Find . d. Find .

P5 ⱕ y ⬍ 9 Py ⱖ 8 Py ⱕ 3