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- The path that a robot is following on a xy -plane is found by interpolating four data points 16. Chapter 3 as follow. X y 2 7.5 4.5 7.5 5.5 6 7 Answer: a) R(x)=0.1524x³-2.5238x² +11.6048x-6.8333. b) P(x) dx = 35.9857. 5 a) Construct the Lagrange interpolation polynomial for the degree of three, P(x). b) From the answer in (a), determine the length of the path from x=2 to x = 7. 1 UseAssume that females have pulse rates that are normally distributed with a mean of μ=76.0 beats per minute and a standard deviation of σ=12.5 beats per minute. Complete part a through c a) If 1 adult female is randomly selected. Find the probability that her pulse rate is less than 82 beats per minute (Round to four decimal places as needed) b) If 4 adult females are randomly selected, find the probability that they have a pulse rates with a mean less than 82 beats per minute (Round to four decimal places as needed) c) Why can the normal distribution be used in part (b) even though the sample size don't exceed 30?(options are the image below)Consider a normal distribution curve where 70-th percentile is at 12 and the 45-th percentile is at 7. Use this information to find the mean, μ, and the standard deviation, o, of the distribution. a) με b) σ =
- give the rejection region.Roll a fair 4-sided die. X is the result. Y is that we toss a fair coin X times and count the number of tails Find the joint distribution for X and Y. Find Cov(X,Y).It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game. x 0 2 5 6 y 50 44 33 26 Complete parts (a) through (e), given Σx = 13, Σy = 153, Σx2 = 65, Σy2 = 6201, Σxy = 409, and r ≈ −0.991 (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r =