Discrete Probability: What is the expected outcome of a hypergeometric distribution in which 10 objects are selected from 40 objects, of which 8 are successes?
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- Many track hurdlers believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The data lists the number of wins for track hurdlers in the different starting positions. Calculate the chi-square test statistic x to test the claim that the probabilities of winning are the same in the different positions. Use α = 0.05. The results are based on 240 wins. Starting Position 3 4 5 6 1 2 Number of Wins 44 32 33 50 36 45 O A. 6.750 O B. 12.592 O C. 15.541 O D. 9.326 C(e) The manager chooses a new production rate for the assembly line. They claim that the production rate that they have chosen will result in the minimum probability that a randomly selected Choc-pricot is imperfect. After running the assembly line at the new production rate for one day, a quality-control officer randomly selects 80 Choc-pricots and 6 are imperfect. (i) Calculate p, the proportion of Choc-pricots that are imperfect in the sample of 80 Choc-pricots manufactured at the new production rate. (ii) Assuming that a sample size of 80 is large enough for the central limit theorem to apply. determine a 90% confidence interval for the proportion of Choc-pricots that will be imperfect at the new production rate. (iii) Using the confidence interval that you calculated in part (e)(ii), can it be concluded that the manager's claim is false with 90% confidence? Justify your answer. WOSK YOUS METQUESTION: A process for putting chocolate chips into cookies is random and the number of choc chips in a cookie has a Poisson distribution with mean A. Find an expression for the probability that a cookie contains less than 3 choc chips.
- Don't hand writingBernoulli process: i.Draw the probability distributions (pdf) for X∼bin (8, p) (x) forp = 0.25, p = 0.5, p = 0.75, in each diagram.ii.What kind of effect has a higher value on the graph , compared to a lower value? iii.You should strike a coin8gonger. You win if there are precise4 or precise5 coins, but otherwise lose. You can choose between three different coins, medpn = P (coin) respectively p1 = 0.25, p2 = 0.5, andp3 = 0.75. Which of these coins gives you the highest probability of winning?Let A, B and C be events from a common sample space such that: P(A) = 0.72, P(B) = 0.56, P(C) =0.25, P(ANB) = 0.42. P(ANC) = 0.18, P(BOC) =0 %3D Compute P(AUBUC).
- The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 15 Southwest flights and observing whether they arrive on time. (a) Find the probability that at least 4 flights arrive on time. (b) Would it be unusual for Southwest to have 3 flights arrive late?(Enter YES or NO)For each probability and percentile problem, draw the picture.A random number generator picks a number from 1 to 8 in a uniform manner. Part (e) ? = rounded to two decimal places) Part (f) P(3.5 < X < 7.25) = (Enter an exact number as an integer, fraction, or decimal.) Part (g) P(X > 3.67) = (rounded to two decimal places)A random sample statistic will have a probability distribution that is its sampling distribution True False
- Of the students in the college, 60% of the students reside in the hostel and 40% of the students are day scholars. Previous year result reports that 30% of all students who stay in the hostel scored A Grade and 20% of day scholars scored A grade. At the end of the year, one student is chosen at random and found that he/she has an A grade. What is the probability that the student is a hostlier?If the probability of a machine producing a defective part is 0.01, what is the probability of finding exactly 1 defective part from a sample of 10? (Assume that the process follows a binomial distribution)
