A business calculates that 60% of its suppliers are UK-based. Every month it randomly selects 8 of its suppliers and checks their compliance with money-laundering legislation. It defines the random variable X to represent how many of the 8 selected supplie are UK-based. This scenario is modelled with a Binomial distribution denoted X- Bin(n, p). (a) State the value of n (b) State the value of p, writing your answer as a decimal to 1 decimal place. (C) How many combinations of 5 UK-based suppliers are possible within the set of 8 suppliers selected for the compliance checks?
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- You roll five fair six-sided dice. Let X denote the sum of the numbers shown. Compute the expectation and the variance of X.very morning, Laura practices shooting basketball free throws. She doesn’t shoot a fixed amount, instead she keeps shooting free throws until she makes 12. Suppose Laura is an 82% free throw shooter. Let X be how many free throws Laura will miss tomorrow morning. Then X has a negative binomial distribution. What is a trial? What is a success? How many successes are required? r = What is the success probability? p =Instructor-created question Question Help A study of 420,051 cell phone users found that 132 of them developed cancer of the brain or nervous system. Complete parts (a) and (b). a. Use the sample data to construct a 90% confidence interval estimate of the percentage of cell phone uners who develop cancer of the brain or nervous system. (Round to three decimal places as needed.) b. Prior to this study of cell phone use, the rate of such cancer was found to be 0.0247% tor those not using cell phones Do cell phone users appear to have a rate of cancer of the brain or nervous system that is different from the rate of such cancer among those not using cell phones? Why or why not? OA. No, because 0.0247% is included in the confidence interval OB. Yes, because 0.0247% is included in the confidence interval OC. No, because 0 0247% is not included in the confidence interval. OD. Yes, because 0.0247% is not included in the confidence interval nts
- A private hospital gets an average of 14 hospital admissions per week in its emergency room (ER). Let x be the outcome of hospital admissions in the emergency room in a week. In order to plan for the number of beds for the future, the hospital has to model the data with an appropriate distribution. (a) what distribution would you suggest for the random variable X, and why? (b) what is the probability of getting at most two admissions in one week? (c) what is the probability of getting at most two admissions in two weeks? (d) what is the probability of getting at least one admission in 2 days, assuming its ER opens 7 days a week? (e) if the hospital closes for three days because of a very serious event, how may new patients will the ER miss for admission on average, in those three days?Imagine that you are training to run a half-marathon and so every week you have 2 intense days, 3 light days, and 2 rest days. On your intense days you run 16 km, on your light days you run 5 km, and on your rest days you do not run. How would you model your miles run per day as a random variable? (Hint: probability distribution)Company F sells fabrics known as fat quarters, which are rectangles of fabric created by cutting a yard of fabric into four pieces. Occasionally the manufacturing process results in a fabric defect. Let the random variable X represent the number of defects on a fat quarter created by Company F. The following table shows the probability distribution of X. X 0 1 2 3 4 or more Probability 0.58 0.23 0.11 0.05 0.03 If a fat quarter has more than 2 defects, it cannot be sold and is discarded. Let the random variable Y represent the number of defects on a fat quarter that can be sold by Company F. (a) Construct the probability distribution of the random variable Y. (b) Determine the mean and standard deviation of Y. Show your work. Company G also sells fat quarters. The mean and standard deviation of the number of defects on a fat quarter that can be sold by Company G are 0.40 and 0.66, respectively. The fat quarters sell for $5.00 each, but are discounted by…
- Five percent of U.S. employees who are late for work blame oversleeping. You randomly select four U.S. employees who are late for work and ask them whether they blame oversleeping. The random variable represents the number of U.S. employees who are late for work and blame oversleeping. Find the mean of the binomial distribution. μ= (Round to the nearest hundredth as needed.)A survey asks 1200 workers, "Has the economy forced you to reduce the amount of vacation you plan to take this year?" Forty-six percent of those surveyed say they are reducing the amount of vacation. Twenty workers participating in the survey are randomly selected. The random variable represents the number and list the possible values of the random variable x. workers who are reducing the amount of vacation. Decide whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q. Is the experiment a binomial experiment? Yes O No What is a success in this experiment? O Selecting a worker who is not reducing the amount of vacation O Selecting a worker who is reducing the amount of vacation O This is not a binomial experiment. Specify the value of n. Select the correct choice below and fill in any answer boxes in your choice. OA n= O B. This is not a binomial experiment. Specify the value of p. Select the correct choice below and fill in any…Provide an example of a binomial random variable and explain how each condition for the binomial distribution is fulfilled.
- Each trial in a binomial experiment has a 25% probability of success.if the normal distribution is to be used to calculate a probability for thisbinomial experiment, then number of trials must be at leastDetermine whether the given procedure results in a binomial distribution. If not, give the reason why not. Choosing marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time with replacement, keeping track of how many marbles are drawn until a red marble is chosen O Not binomial; there is not a fixed number of trials O Not binomial; there are more than two outcomes for each trial O Not binomial; the trials are not independent O Not binomial; for more than one of the reas as given in the above answer choices O This procedure results in a binomial distribution Submit Question X PrtScn DII F3 4 R F4 % 5 T F5 6 F6 & 7 U F7 * 8 F8 Home ( F9 O ) End F10 P32% of working mothers do not have enough money to cover their health insurance deductibles. You randomly select six working mothers and ask them whether they have enough money to cover their health insurance deductibles. The random variable represents the number of working mothers who do not have enough money to cover their health insurance deductibles. Complete parts (a) (a) Construct a binomial distribution using n=6 and p=0.32. x P(x) 0 1 2 3 4 5 6 (Round to the nearest thousandth as needed.)