Problem 2. Find P[K < E[K]] when K is Geometric (2/5). K is Binomial (8, 1/4). K is Poisson (6). K is discrete uniform (1, 11). a. b. c. d.
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![Problem 2.
Find P[K < E[K]] when
K is Geometric (2/5).
K is Binomial (8, 1/4).
K is Poisson (6).
K is discrete uniform (1, 11).
a.
b.
c.
d.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a344ceb-d884-4942-ba8b-5777ad740f66%2F3b7ce288-9674-4451-9bca-23f5f9c45b4c%2Fwxjmzs.png&w=3840&q=75)
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- Question 4a. A large accountancy firm finds that over the long run 10% of its statements for clients are in error in some way. A quality assurance officer at the firm investigating the source of the errors takes a sample of 20 statements produced by a single employee and classifies each as being “in error” or “not in error”.i. If the variable X is used to represent the number of statements in the sample that are in error, and assuming the error rate is the firm’s level of 10% then state:• the type of distribution this variable has; and• the parameter/s of this distribution. ii. Determine the probability that 2 or less returns in this sample are in error. The quality assurance officer found that there were 5 statements in the sample that were in error.iii. Determine the probability of finding 5 or more returns in error if indeed the error rate was 10%. iv. Based upon your answer for part iii., what conclusion might the quality assurance office make about this employee in terms of the…Question 15: In a recent Super Bowl, a TV network predicted that 90 % of the audience would express an interest in seeing one of its forthcoming television shows. The network ran commercials for these shows during the Super Bowl. The day after the Super Bowl, and Advertising Group sampled 55 people who saw the commercials and found that 48 of them said they would watch one of the television shows.Suppose you are have the following null and alternative hypotheses for a test you are running:H0:p=0.9H0:p=0.9Ha:p>0.9Ha:p>0.9Calculate the test statistic, rounded to 3 decimal places z=Suppose X is binomially distributed with parameters n and p; further suppose that E(X) = 5 and Var(X) = 4. Find the n and p.
- Find P[K < E[K]] whena) K is geometric (1/3).b) K is binomial (6, 1/2).c) K is Poisson (3).d) K is discrete uniform (0, 6).Question 5 According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. Use the Bayes Theorem to calculate the probability that annual household income is at most $25,000 if the residents of a household do not own 2 cars.Each of 14 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppose that 9 of these refrigerators have a defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order, let X be the number among the first 6 examined that have a defective compressor. (I have figured out part "a" but need help with "b" and P(X ≤ 3) in "c") (a) Calculate P(X = 4) and P(X ≤ 4). (Round your answers to four decimal places.) P(X = 4) = P(X ≤ 4) = (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.) (c) Consider a large shipment of 400 refrigerators, of which 40 have defective compressors. If X is the number among 25 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately)…
