2. A random experiment consists of tossing a die and observing the number of dots showing up. Let A₁: number of dots showing up=3 A2: even number of dots showing up A3: odd number of dots showing up Find P(A₁) and P(A₁A3) Find P(A₂A3), P(A₂ A3), P(A₁ | A3)
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- A manufacturing company that produces laminate for countertops is interested in studying the relationship between the number of hours of training that an employee receives and the number of defects per countertop produced. Ten employees are randomly selected. The number of hours of training each employee has received is recorded and the number of defects on the most recent countertop produced is determined. The results are as follows. Hours of Training Defects per Countertop 1 5 4 1 7 0 3 3 2 5 2 4 5 1 5 2 1 8 6 2 Copy Data The estimated regression line and the standard error are given. Defects per Countertop=6.717822−1.004950(Hours of Training)se=1.229787se=1.229787 Suppose a new employee has had 5 hours of training. What would be the 90% prediction interval for the number of defects per countertop? Round your answer to two decimal places.Allergic reactions to poison ivy can be miserable. Plant oils cause the reaction. Researchers at Allergy Institute did a study to determine the effects of washing the oil off within 5 minutes of exposure. A random sample of 1000 people with known allergies to poison ivy participated in the study. Oil from the poison ivy plant was rubbed on a patch of skin. For 500 of the subjects, it was washed off within 5 minutes. For the other 500 subjects, the oil was washed off after 5 minutes. The results are summarized in the following table. Reaction Within 5 Minutes After 5 Minutes Row Total NoneMildStrong 4025543 64323113 466378156 Column Total 500 500 1000 Let's use the following notation for the various events: W = washing oil off within 5 minutes, A = washing oil off after 5 minutes, N = no reaction, M = mild reaction, S = strong reaction. Find the following probabilities for a person selected at random from this sample of 1000 subjects. (Use 3 decimal places.) (d) P(N and…Assume that a coin is tossed twice. The coin may not be fair. The sample space consists of the outcomes {HH, HT, TH, TT}.
- A recent poll indicates that 48% of all registered voters in America plan to vote for a specific candidate in the upcoming presidential election. Suppose a random sample of 20 Americans is taken. Let X represent the sample count who plan to vote for the candidate. What is P(X≠5)? An experiment consists of drawing two numbers out of a hat one after the other containing the numbers 1, 3, 5, 6. The two numbers are then recorded as a 2-digit number. The number drawn is NOT put back in the hat before drawing the second. Do the following: List the sample space.________________________________ Let F = the event of getting a number whose first digit is odd Let S = the event of getting a multiple of 6 Find P( F and S) =____________________________________ Find P(F) =______________________________ Find P(F|S) =_______________________________________ Are F and S independent events? ___________Justify_____________ VIII (15) Let E be the event that at least two people out of 4 have the same birth month (not day). How many outcomes in the Sample space. In other words, compute n(S).________ State in words the complement of E. _____________________________ How many outcomes in the event not E. In other words, compute n(not E). ________…A building contractor has a chance to buy an odd lot of 1,000 used bricks at an auction. She is interested in determining the proportion of bricks in the lot that are cracked and therefore unusable for her current project, but she does not have enough time to inspect all 1,000 bricks. Instead, she checks 150 bricks to determine which ones are cracked. What is the population of interest? all building contractors all 1,000 bricks in the lot the rest of the 850 bricks the 150 bricks selected for inspection the rest of the 700 bricks What group constitutes the sample? the 150 bricks selected for inspection all building contractors the rest of the 700 bricks all 1,000 bricks in the lot the rest of the 850 brickS Submit Answer
- A fair coin is tossed three times. Let X be number of heads. (1) Write out the sample space. (2) Find P(X=2) (3) Find E(X)Itranscript One male and one female dam rat pup were randomly selected from 8 litters to perform the swim maze. Each pup was placed in the water at one end of the maze and allowed to swim until it escaped at the opposite end. If the pup failed to escape after a certain period of time, it was placed at the beginning of the maze and given another chance. The experiment was repeated until each pup accomplished three successful escapes. The table to the right reports the number of swims required by each pup. Is there sufficient evidence of a difference between the mean number of swims required by male and female pups? Use a=0.01. Comment on the assumptions required for the test to be valid. B. t> Litter 1 2 3 OC. t 10 12 Female 11 [6526675 10. Assume that the box contains balls numbered from 1 through 28, and that 3 are selected. A random variable X is defined as 3 times the number of odd balls selected, plus 4 times the number of even. How many different values are possible for the random variable X?