On a certain hole, a golfer knows that he has a 70% chance of reaching the green (putting surface) in one stroke, 20% in two strokes, 8% in three, and 2% in four or more. If he reaches the green on his first stroke, he has an 80% chance of putting the golf ball in the cup on his second stroke. If he does not reach the green on his first stroke, then he has a 30% chance of putting the golf ball in the cup on his second stroke. What is the probability that the golfer will reach the green in one stroke and put the ball in the cup on his second stroke? 0.09 0.21 0.56 0.80

Certain app allows you to order from different types of cuisine. According with the app's records 23% of the orders are to an American food restaurant, 38% to an Asian food restaurant, 17% to a Mexican food restaurant, 6% to a Dessert place, and the rest are to other types of restaurants. Assume that incoming orders are independent of each other.

not A 1995 study by the School of Public Health reported that 87% of male students who live in a fraterity house are binge drinkers. The figure for fraternity members who are residents of a fraternity house is 71 %, while the figure for men who do not belong to a fraternity is 44 % Suppose that 11% of U.S. male students live in a fraternity house, 15% belong to a fraterity but do not live in a fraterity house, and 74% do not belong to a fraterity a. What is the probability that a randomly selected malp student is a binge drinker? b. If a randomly selected male student is a binge drinker, what is the probability that he lives in a fraterity house? The probability that a randomly selected male student is a binge drinker is 0.5509 (Type an integer or a decimal rounded to two decimal places as needed) CETTE

A small computer lab has 2 terminals. The number of students working in this lab is recordedat the end of every hour. A computer assistant notices the following pattern:- If there are 0 or 1 students in a lab, then the number of students in 1 hour has a50-50% chance to increase by 1 or remain unchanged. - If there are 2 students in a lab, then the number of students in 1 hour has a 50-50%chance to decrease by 1 or remain unchanged.  (a) Write the transition probability matrix for this Markov chain.(b) Suppose there is nobody in the lab at 7 am. What is the probability of nobody workingin the lab at 10 am?

There are two bags A and B. Bag A contains n white balls and 2 black balls while bag B contains 2 white balls and n black balls. One of the two bags is selected at random and two balls are drawn from it without replacement. We know that if both the balls drawn are white balls, the probability of bag A being selected to draw the balls is . Find the value of n.

Mateo believes that completely cutting caffeine out of a person's diet will allow them more restful sleep at night. He randomly selects 8 adults to help him test this theory. Each person is asked to consume two caffeinated beverages per day for 28 days and then cut back to no caffeinated bevarages for an additional 28 days. During each period, the participants record the number of nights of restful sleep that they had. The following table gives the results of the study. Test Mateo's claim at the 0.05 level of significance. Give answers to 4 decimal places as needed. Number of Nights of Restful Sleep in a Four-Week Period 15 With Caffeine 21 20 22 24 18 21 24 20 26 26 22 21 23 27 23 Without Caffeine a) The normal probability plot showed the differences follow a normal distribution and the boxplot showed no outliers. b) Test the claim (1) Determine the null and alternative hypotheses. Enter correct symbol and values Ho: H₁: (2) Type of test: (3) a = (4) Test statistic (to) = p-value =…

You randomly recruit 23 students and tell each of them to come to the lab in two different mornings: each morning they will be offered some breakfast and will take a test. Each student will receive the light breakfast one time and the nutritious breakfast the other time (some will receive the light breakfast first, the others will receive the nutritious breakfast first, and the second time they switch). The average difference in a student’s score after eating the nutritious breakfast and their score after eating a light breakfast is 4.5, and the standard deviation of this difference is 3.6. (a)  Construct a 95% confidence interval for the difference in the average score of students after having a nutritious breakfast and the average score of students after having a light breakfast.

XYZ Construction Company has three loaders operating every day in a construction site. During any day, each loader that is operating at the beginning of the day has a 0.25 chance of breaking down. If a loader breaks down during the day, it is sent to a repair station and will be working (operational) two days after it breaks down. (Thus, if a loader breaks down during day 3, it will be working at the beginning of day 5. Let the state of the system be the number of operational loaders at the beginning of the day. How many states does the system have?