Solve the question

Consider the drying time data for Exercise 1.1 on page 13. Compute the sample variance and sample standard deviation. Reference: Exercise 1.1 The following measurements were recorded for the drying tine. in hours. of a certain brand of latex pa'nt. 3.4 2.5 4.8 2.9 3.6 2.8 3.3 5.5 3.? 2.3 4.4 4.0 5.2 3.0 4.3 Assume that the measurements are a simple random sample. {a} What is the sample size for the above sample? {In} Calculate the sample mean for these data. {c} Calculate the sample median. {djl Plot the data by way of a dot plot. {e} Compute the 20% trirm'ned mean for the above data set. { Is the sample mean for these data more or less descriptive as a center of location than the trimmed mean? A cereal manufacturer is aware that the weight of the product in the box varies slightly from box to box. In fact, considerable historical data have allowed the determination of the density function that describes the probability structure for the weight (inounces). Letting X be the random variable weight, in ounces, the density function can be described as (a) Verify that this is a valid density function. (b) Determine the probability that the weight is smaller than 24 ounces. (c) The company desires that the weight exceeding 26 ounces be an extremely rare occurrence. What is the probability that this rare occurrence does actually occur? A shipment of 7 television sets contains 2 defective sets. A hotel makes a random purchase of 3 of the sets. If x is the number of defective sets purchased by the hotel, find the probability distribution of X. Express the results graphically as a probability histogram.From a box containing 4 black balls and 2 green balls, 3 balls are drawn in succession, each ball being replaced in the box before the next draw is made. Find the probability distribution for the number of green balls. A typical roulette wheel used in a casino has 38 slots that are numbered 1, 2, 3, . . ., 36, 0, 00, respectively. The 0 and 00 slots are colored green. Half of the remaining slots are red and half are black. Also, half of the integers between 1 and 36 inclusive are odd, half are even, and 0 and 00 are defined to be neither odd nor even. A ball is rolled around the wheel and ends up in one of the slots; we assume that each slot has equal probability of 1/38, and we are interested in the number of the slot into which the ball falls. (a) Define the sample space S. (b) Let A = {0, 00). Give the value of P (A). (c) Let B = {14, 15, 17, 18). Give the value of P (B). (d) Let D = {x : x is odd). Give the value of P (D).Find the probability distribution for the number of jazz CDs when 4 CDs are selected at random from a collection consisting of 5 jazz CDs, 2 classical CDs, and 3 rock CDs. Express your results by means of a formula. A tire manufacturer wants to determine the inner diameter of a certain grade of tire. Ideally, the diameter would be 570 mm. The data are as follows: 572, 572, 573, 568, 569, 575, 565, 570. (a) Find the sample mean and median. (b) Find the sample variance, standard deviation, and range. (c) Using the calculated statistics in parts (a) and (b), can you comment on the quality of the tires?Find the cumulative distribution function of the random variable Win Exercise 3.8. Using A(w), find (@) P(W = 0); (b) P(-1 s W