Suppose that the PDF for the number of years it takes to earn a Bachelor of Science (B.S.) degree is given in Table P(x) 3 0.05 4 0.40 5 0.30 6 7 0.15 0.10 Table a. In words, define the random variable X. b. What does it mean that the values zero, one, and two are not included for x in the PDF?

Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail. 16 6 8 9 10 18 14 13 9 10 25 18 13 8 14 3 The sample mean is x = 12.1%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use ? = 0.01. (a) What is the level of significance?   Compute the z value of the sample test statistic. (Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Providence, RI has the best donuts in the U.S., it’s no question! Consider the following pdfs regarding the two competing bakeries in Providence. Let the random variables X and Y represent the number of donuts produced per hour in which the donut hole was not punched out for bakery X and bakery Y, respectively.   X,Y 0 1 2 3 4 5 P(x) .91 .04 .01 .02 .01 .01 P(y) .67 .21 .04 .05 .01 .02   Given that by 12:30pm (i.e. within the last 30 minutes of the current “hour”) bakery Y has produced 1 donut in which the donut hole was not punched out, what is the probability that they will produce more than 3 donuts in which the donut hole was not punched out by the end of the current “hour” (1pm)? a.) 24% b.) 9% c.) 14% d.) 22% e.) 50%

Part 2 Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information. x 0.338 0.306 0.340 0.248 0.367 0.269 y 3.5 7.7 4.0 8.6 3.1 11.1  Σx = 1.868, Σy = 38, Σx2 = 0.592034, Σy2 = 294.32, Σxy = 11.1556, and r ≈ -0.901. Se ≈ 1.5890, a ≈ 26.420, and b ≈ -64.517. (a) Find the predicted percentage  of strikeouts for a player with an x = 0.328 batting average. (Use 2 decimal places.) %(b) Find a 90% confidence interval for y when x = 0.328. (Use 2 decimal places.) lower limit  % upper limit  %

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond). For the past several years, we have the following data. x: 15 0 24 28 15 17 36 −9 −16 −16 y: 21 −8 27 10 10 27 22 −2 −3 −1

Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail. 15 7 7 13 13 20 13 12 5 10 26 22 13 7 11 3 The sample mean is x = 12.3%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use α = 0.01. (a) What is the level of significance? Compute the z value of the sample test statistic. (Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

A pathologist has been studying the frequency of bacterial colonies within the field of a microscope using samples of throat cultures from healthy adults. Long-term history indicates that there is an average of 2.80 bacteria colonies per field. Let r be a random variable that represents the number of bacteria colonies per field. Let O represent the number of observed bacteria colonies per field for throat cultures from healthy adults. A random sample of 100 healthy adults gave the following information. 2 3 4 5 or more 13 18 28 16 17 8 (a) The pathologist wants to use a Poisson distribution to represent the probability of r, the number of bacteria colonies per field. The Poisson distribution is given below. P(r) = r! Here 1 = 2.80 is the average number of bacteria colonies per field. Compute P(r) for r = 0, 1, 2, 3, 4, and 5 or more. (Round your answers to three decimal places.) P(0) = P(1) = Р(2) Р(3) 3 P(4) = %3D P(5 or more) = (b) Compute the expected number of colonies E = 100P(r)…

Total blood volume (in ml) per body weight (in kg) is important in medical research. For healthy adults, the red blood cell volume mean is about u = 28 ml/kgt. Red blood cell volume that is too low or too high can indicate a medical problem. Suppose that Roger has had seven blood tests, and the red blood cell volumes were as follows. 31 26 43 37 32 38 29 Let x be a random variable that represents Roger's red blood cell volume. Assume that x has a normal distribution and o = 4.75. Do the data indicate that Roger's red blood cell volume is different (either way) from u = 28 ml/kg? Use a 0.01 level of significance. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? O Ho: H = 28 ml/kg; H,: µ > 28 ml/kg; right-tailed O Ho: H = 28 ml/kg; H,: u < 28 ml/kg; left-tailed O Họ: H + 28 ml/kg; H,: µ = 28 ml/kg; two-tailed O Ho: H = 28 ml/kg; H,: µ + 28 ml/kg; two-tailed (b) What sampling distribution will you…