A worn machine is known to produce 10% defective components. If the random variable X is the number of DEFECTIVE components produced in a run of 4 components. Compute the probability of P(X=3)
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- A student needs to know the details of a class assignment that is due the next day and decides to call her class members for this information. She believes that for any particular call, the probability of obtaining the necessary information is 0.2. She decides to continue calling class members until the information is obtained. However, her cell phone is old, and her battery will not last for more than 12 calls. Let the random variable X be the number of calls needed to obtain the information. What is the probability that at least three calls are required?Find the expected value and the variance of the number of times one must throw a die until the outcome 1 has occurred 4 times.Total blood volume (in ml) per body weight (in kg) is important in medical research. For healthy adults, the red blood cell volume mean is about µ = 28 ml/kg. Red blood cell volume that is too low or too high can indicate a medical problem. Suppose that Roger has had seven blood tests, and the red blood cell volume sample mean was 32.7 ml/kg. Let x be a random variable that represents Roger’s red blood cell volume. Assume that x has a normal distribution and = 4.75. Do the data indicate that Roger’s red blood cell volume is different (either way) from µ = 28 ml/kg? use a 0.01 level of significance.
- An IT company employs two sales engineers. Engineer 1 does the work of estimating cost for70% of jobs bid by the company. Engineer 2 does the work for 30% of jobs bid by the company.It is known that the error rate for engineer 1 is such that 0.02 is the probability of an error whenhe does the work, whereas the probability of an error in the work of engineer 2 is 0.04. Supposea bid arrives and a serious error occurs in estimating cost. Which engineer would you guess didthe work? Explain and show all work.We are picking 200 jelly beans out of a huge vat at a factory known to have 25% black jelly beans. Use the normal approximation to the binomial to find the probability that we get 60 or fewer black jelly beansSuppose you were selected from a population at random to take a medical test. It is believed that there is a 5% chance that you are ill (i.e. you have the disease), since that is the disease prevalence for asymptomatic people like yourself. Suppose that the test you take has some error rate. If you are ill, it will correctly identify you as positive 90% of the time. If you not ill, it will give a false positive 2% of the time. What is probability that you are ill given a positive test result?
- Based on the survey assume that 49% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that 5 consumers are randomly selected exactly 2 of them are comfortable with delivery by drones. Indemnify values of n, x, p, and q.A construction company employs two sales engineers. Engineer 1 does the work of estimating cost for 70% of jobs bid by the company. Engineer 2 does the work for 30% of jobs bid by the company. It is known that the error rate for engineer 1 is such that 0.02 is the probability of an error when he does the work, whereas the probability of an error in the work of engineer 2 is 0.04. Suppose a bid arrives and a serious error occurs in estimating cost. What is the probability that Engineer 1 did the work?The probability of a positive reaction of the patient to a test developed against a disease is 0.4. Calculate the probability that the first positive response will occur in experiment 5.
- The fraction of a large population that has a specific blood type T is .08 (8%). For blood donation purposes it is necessary to find 4 people with type T blood. If randomly selected individuals from the population are tested one after another, then (a) What is the probability y persons have to be tested to get 5 type T persons, and (b) What is the probability that over 80 people have to be tested?I have 3 chickens where each of these chickens lays an egg with the probability 3/4 (independently). I sell each egg the chicken has laid for 8 coins. Work out the variance of the number of coins recieved.From observations of the weather, it is known that on October 20 the probability of rain is 0.85. A certain forecast method for October 20 is correct 0.9 times if rain is predicted and 0.75 times if no rain is predicted. How much information does a real weather forecast provide 20 th of October?
