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- aaaaaa A soft drink machine outputs a mean of 27 ounces per cup. The machine's output is normally distributed with a standard deviation of 3 ounces. What is the probability of filling a cup between 21 and 30 ounces? Round your answer to four decimal places.The probabilities of X, Y and Z becoming managers are 4/9, 2/9 and 1/3 respectively. The probabilities that the Bonus Scheme will be introduced if X, Y and Z becomes managers are 3/10, 1/2, and 4/5 respectively. (i) What is the probability that Bonus Scheme will be introduced, and (ii) if the Bonus Scheme has been introduced, what is the probability that the manager appointed was X ?6.33 Statistics released by the National HighwayTraffic Safety Administration and the National SafetyCouncil show that on an average weekend night, 1 outof every 10 drivers on the road is drunk. If 400 driversare randomly checked next Saturday night, what is theprobability that the number of drunk drivers will be(a) less than 32?(b) more than 49?(c) at least 35 but less than 47?
- A market research firm is interested in surveying certain attitudes in a small community. There are 125 households broken down according to income, ownership of a telephone or ownership of a T.V. Household with monthly Household with monthly 8.000 income of " 8,000 or less Telephone Subscriber income above No Telephone Telephone SubsNcriber No. Telephone Own 7V. set 27 20 18 10 No. T.V. set 18 10 12 10 (i) What is the probability of obtaining of a TV. owner in drawing at random ? (ii) If a household has monthly income over Rs. 8,000 and is a telephone subscriber, what is the probability that it has a T.V. ? (iii) What is the conditional probability of drawing a household that owns a T.V., given that the household is a telephone subscriber ? (iv) Are the events 'ownership of a T.V.' and 'telephone subscriber statistically independent ? Comment.Please no written by hand solution Kate recently invested in real estate with the intention of selling the property one year from today. She has modeled the returns on that investment based on three economic scenarios. She believes that if the economy stays healthy, then her investment will generate a 30 percent return. However, if the economy softens, as predicted, the return will be 10 percent, while the return will be -25 percent if the economy slips into a recession. If the probabilities of the healthy, soft, and recessionary states are 0.6, 0.2, and 0.2, respectively, then what are the expected return and the standard deviation of the return on Kate❝s investment? Calculate the coefficient of variation for this investment. (Round expected return to 3 decimal places, e.g. 0.125 and round intermediate calculations and standard deviation to 5 decimal places, e.g. 0.07680.)Find the probability of rolling a standard 6-sided die 23 times and getting 10 or more twos. Select an answer Enter a decimal rounded to four places as needed.
- Question Two a) The table below shows the probability distribution of the discrete random variable X. 2 3 4 5 7 P(X=x) 2p 2p 3p i. Find the value of p from the table above. Calculate the probability that at X is at least 5. Calculate the mean of the distribution. ii. 111.7. A sample of n values is drawn from a population whose probability density is ae-ax, (x 2 0, a > 0). If X is mean of the sample, show that na X is a y (n) variate 1 that E(X) and S.E. of (X) = avn 1 and prove aWhat do we call the probability of a Type I error?
- Suppose that a family has 4 chilidren. Also, suppose that the probability of having a boy is Find the probability that the family has at least 3 boys. The probability that the family has at least 3 boys is (Type an integer or a simplified fraction,)Two factories mamufacture the Number of Defects same machine parts. Each part is classified as having either 0, 1, 2 or 3 mamufacturing defects. The joint probability for this is given in the adjoining Table. (i) A part is observed to have no defect. What is the probability that it was produced by X mamufacturer ? Manufacturer 21 3 0-1250 0-0625 0-1875 0-1250 Y 0-0625 0-0625 0-1250 0-2500 (ii) A part is known to have been produced by mamufacturer X. What is the probability that the part has no defects ? (iii) A part is known to have two or more defects. What is the probability that it was manufactured by X? (iv) A part is known to have one or more defects. What is the probability that it was manufactured by Y ?Exercise 15:- Each unit of a product produced and sold earns a profit of Rs. 50 and unsold units result into a loss of Rs. 30. The probability distribution is given below :Units Demanded : 0 1 2. 3.Probability : 0.2. 0.2. 0.25. 0.3Calculate EPPI and EVPI.