∙ Based on the relative frequency assessment method, what is the probability that manufactured item is blue? o P(blue)=.3371 ∙ What is the probability that the product manufactured is an ro-50 o P(ro-50)=.6056 ∙ What is the probability that a product manufactured is a ro 50 and blue? o P(ro-50 and blue)=.2986 1. Question 4 a. A successful barbecue chain sells its beef, pork, and chicken items to three kinds of customers: dine-in, delivery, and pickup. Last year’s sales showed that 12,762 orders were dine-in (d), 5,895 were delivery orders €, and 3,133 orders were pickup (p). Suppose an audit of last year’s sales is being conducted. Complete parts a through c. i. If a customer order is selected at random, what is the probability it will be a pickup order? 1. P(pickup)=.1438 ii. What method of probability assessment is used to determine the probability in part a? 1. Relative frequency assessment iii. If two customer orders are selected at random, list the sample space indicating the type of order for both customers 1. (d, d), (d, e), (d, p), (e, d), (e, e), (e, p), (p, d), (p, e), (p, p) 2. Question 5 a. A company produces scooters used by small businesses that find them convenient for making short deliveries. The company is notified whenever a scooter breaks down, and the problem is classified as being either mechanical or electrical. The company then matches the scooter to the plant where it was assembled. The data table to the right contains a random sample of 200 breakdowns. Use the data file and the relative frequency assessment method to complete parts a through c.
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1. What is the probability a scooter was assembled at plant 2? a. P(plant 2).665 2. What is the probability that a scooter breakdown was due to a mechanical problem? a. P(mechanical)= .52 3. What is the probability that a scooter breakdown was due to an electrical problem and the scooter was assembled at plant 1?a. P(electrical and plant 1)=.105 1. Question 6 a. Three events occur with probabilities p (e1) =.38, p (e2) =.17, and p (e3) =.46. If the event B occurs, the probability becomes P (e1b) = .23, P (b) =.28. Complete parts a through c. i. Calculate P (E1 and B) 1. Use technology or the formula for the Multiplication Rule shown below, where A1 and A2 are and two events, to find the probability of the event. a. P(A1 and A2) = P (A1) P (A2|A1) 2. What is P (B) a. = .28 3. What is P (E1B) a. =.23 4. Substitute P (B)=.28 and P (E1|B)=.23 into the formula from the previous step to calculate P (E1 and B) a. P (E1 and B) = P (B)P (E1|B) i. =.28*.23 1. =.0644 ii. Use technology or the formula for the addition rule shown below, where A1 and A2 are any events, to find the probability of the event. 1. P (A1 or A2)= P (A1) + P(A2) – P (A1 and A2) a. P (E1 or B)= P (E1) + P (B) – P ( E1 and B) i. =.38 +.28 -0.0644 1. =.5956 iii. Use technology or the formula for the multiplication rule for independent events shown below, where A1 and A2 are any tow events, to find the probability of the event. 1. P (A1 and A2) =P (A1) P(A2) 2. P (E1 and E2 and E3) = P (E1) P(E2) P(E3) a. =.38*.17*.46 i. .0297 2. Question 7 a. The table to the right gives a breakdown of 2,167 civil cases that were appealed. The outcome of theappeal, as well as the type of trial (judge or jury), was determined for each case. Suppose one of the cases is selected at random and the outcome of the appeal and type of trial are observed. Complete parts a through c.
Plaintiff trial win reversed
Plaintiff trial win affirmed/dismissed
Defendant trial win-reversed
Defendant trial win affirmed/dismissed
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1. What is the probability that a randomly selected case is a judge trial? a. The probability that a random selected case is a judge trial is i. .318 b. What is the probability that the final outcome of a randomly selected case is “plaintiff trial win is reversed? i. .126 c. If a randomly selected case is a jury trial, what is the probability that the final outcome of the case is a plaintiff trial win?.
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