e 16-20. In order to test whether a coin is perfect, it is tossed 5 times. The null hypothesis of nerfectness is rejected if and only if more than 4 heads are obtained. Obtain the (i) critical region, (ii) probability of type I error, and (iii) probability of type II error, when the corresponding probability of getting a head is 0-2.
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- Muscular dystrophy is a genetic disease caused by a mutation on the X chromosome. During reproduction this mutation arises spontaneously on each of the X chromosomes of the parents, independently and with probability μ = 0.888. We can therefore view the production of a child as consisting of two probabilistic experiments. First, one of the two sex chromosomes is chosen with equal probability from each parent. Second, for each X chromosome that is chosen, the muscular dystrophy mutation arises independently with probability M. All male children carrying the mutation will develop muscular dystrophy, whereas only females whose X chromosomes both carry the mutation will develop the disease. What is the probability that a child will develop the disease? Round your answer to five decimal places.A company's records show that 35% of the employees receive a performance bonus. I randomly selects a sample of 5 employees from the company. 11. The probability that none of these employees receive a performance bonus is: A 0.247 В 0.186 C 0.884 0.116 12. The probability that at most 2 of these employees receive a performance bonus is: А 0.678 B 0.808 C 0.706 D 0.765 13. Consider the normal distribution function. The area between z -scores of – 1.56 i A 0.9105 В 0.0293 C 0.856 D 0.9398PM)- Google Chrome va.edu.om/mod/quiz/attempt.php?attempt=818373&cmid%3D121611&page=D5 تجامعتگروی University of Nizwa A coin is tossed four times. The probability of getting more than one tail is OA. 5/8 OB. 11/16 OC. 5/16 OD. 3/8 OE. None of these The probability of getting minimum three heads is Oa. 1/4 Cb.3/4 Oc. 5/16 Cd. 3/8, CE. None of these page
- Two random variables X and Y are independent. Each has a binomial distribution with success probability 0.4 and 2 trials. a) Find the joint probability distribution function f(x,y). b) Give the joint probabilities using a table. Hint, the size of the table is 3 by 3. c) Find the probability P(Y > X).A wine producer claims that the proportion of its customers who cannot distinguish its product from frozen grape juice is, at most, 0.09. The producer decides to test this null hypothesis against the alternative that the true proportion is more than 0.09. The decision rule adopted is to reject the null hypothesis if the sample proportion of people who cannot distinguish between these two flavors exceeds 0.14. a) If a random sample of 100 customers is chosen, what is the probability of a Type I error, using this decision rule? b) If a random sample of 400 customers is selected, what is the probability of a Type I error, using this decision rule? Explain, in words and graphically, why your answer differs from that in part a. c) Suppose that the true proportion of customers who cannot distinguish between these flavors is 0.20. If a random sample of 100 customers is selected, what is the probability of a Type II error?3. A robot is going to attempt the same task 100 times. Each time it tries, it will either succeed or fail to succeed in completing the task. Say the robot does not learn from its tries, so each attempt at the task is independent of the others. On a given attempt, the probability of the robot succeeding is 0.85. Let X be the random variable of the number of times this robot is able to succeed in completing the task. part 1. What is the probability that the robot succeeds less than or equal to 80 times? (it is only for part a; no need to show work) a. Use the compliment rule to reduce the number of operations needed in part 1. Find another way to compute the needed probability. b. Now say two robots are going to attempt the same task. The robots operate independently from one another. What is the probability that both robots succeed less than or equal to 80 times out of 100? c. Now say the single robot begins to learn the more it tries. That is to say, it gets better at succeeding at…
- Q4. A box contains resistors, where 3% of the resistors are deficient because their resistance values are not meeting specifications written on the box. Technicians of the workshop are testing resistors before the resistors are soldered to an electrical circuit. The operators select unusable resistor as a deficient one with a probability of 0.95. However, the operator can incorrectly check a good resistor and assume that it is a deficient one with a probability of 0.05. If a resistor is selected as deficient after it was tested by an operator, what is the probability that the resistor is actually unusable for the electrical circuit? (Use Bayes' Formula)A student randomly guesses at four multiple-choice questions. Each question has three possible choices. The random variable X denotes the number of correct answers. This experiment can be modeled as Oa) a normal experiment with mean 4 and standard deviation 1/3. O b) a normal experiment with mean 1/3 and standard deviation 4. O c) a binomial experiment with 3 trials and success probability 1/4. O d) a binomial experiment with mean 4 and standard deviation 1/3 O e) a binomial experiment with 4 trials and success probability 1/3.Muscular dystrophy is a genetic disease caused by a mutation on the X chromosome. During reproduction this mutation arises spontaneously on each of the X chromosomes of the parents, independently and with probability μ = 0.805. We can therefore view the production of a child as consisting of two probabilistic experiments. First, one of the two sex chromosomes is chosen with equal probability from each parent. Second, for each X chromosome that is chosen, the muscular dystrophy mutation arises independently with probability μ. All male children carrying the mutation will develop muscular dystrophy, whereas only females whose X chromosomes both carry the mutation will develop the disease. What is the probability that a child will develop the disease? Round your answer to five decimal places.
- A boy uses a homemade metal detector to look for valuable metal objects on a beach. The machine isn't perfect-it identifies only 98% of the metal objects over which it passes, and it identifies 4% of the nonmetallic objects over which it passes. Suppose that 25% of the objects that the machine passes over are metal. Find the probability that the boy has found a metal object when he receives a signal from the machine. Show your work.less than the maximum allowable load for the aircraft. The aircraft can carry 37 passengers, and a flight has fuel and baggage that allows for a total passenger load of 5,957 lb Before every flight, the pilot must verify that the total weight of the load = 161 lb. What is the probability that the aircraft is overloaded? Should the pilot 5,957 Ib. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 37 take any action to correct for an overloaded aircraft? Assume that weights men are normally distributed with a mean of 179.9 lb and a standard deviation of 38.8. The probability is approximately. (Round to four decimal places as needed.) Should the pilot take any action correct for an overloaded aircraft? O A. No. Because the probability is high, the aircraft is safe to fly with its current load. O B. Yes. Because the probability is high, the pilot should take action by somehow reducing the…
