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- Which of the following random variables is discrete? a. W=duration of travel (in minutes) from house to school b. X = proportion of failing subjects of a student in a semester c. Y = number of business permits issued each month in Makati d. Z = weight of dog food (in kilograms) supplied by a certain pet store per month2.2 handwritten Answer letters f, g and hLet 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 0.336 0.296 0.340 0.248 0.367 0.269 y 3.2 7.5 4.0 8.6 3.1 11.1 (b) Use a 10% level of significance to test the claim that ρ ≠ 0. (Use 2 decimal places.) t critical t ± (d) Find the predicted percentage of strikeouts for a player with an x = 0.288 batting average. (Use 2 decimal places.) %(e) Find a 95% confidence interval for y when x = 0.288. (Use 2 decimal places.) lower limit % upper limit % (f) Use a 10% level of significance to test the claim that β ≠ 0. (Use 2 decimal places.) t critical t ± (g) Find a 95% confidence interval for β and interpret its meaning. (Use 2 decimal places.) lower limit upper limit please show steps and work
- 1. Identify if the following scenarios describe a discrete or continuous random variable. Explain your choice. (a) X = The number of persons in an emergency room 181screte (b) W = The weights of delivery trucks at a supermarket. Lconinaas (c) H= The areas of houses being built in a new subdivision. 2. Faith is a 95% free throw shooter. At practice, each player shoots 20 free throws. L X the number of free throws Faith makes out of 20 shots. (a) Explain why X is a binomial random variable. (b) Calculate the mean of X. (c) Calculate the standard deviation of X. (d) Use the binomial probability formula to find P(X = 19). Interpret this value in context. (e) Her coach says that he will let the team out of practice early if Faith makes 18 or me free throws. What is the probability that practice ends early? Show your work. 2017 BFW Publishers Starnes/Tabor Statistics and Probability with Applications 3/eSuppose the random variable Z follows a standard normal distribution. Then the probability is 0.20 that Z is less than the value O a. 0.84 O b. -0.84 O c. - 0.80 Od. 0.80Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with o = 2.4%. A random sample of 10 bank stocks gave the following yields (in percents). 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is u = 4.8%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.8%? Use a = 0.01. (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? Ho: H = 4.8%; H1: µ ± 4.8%; two-tailed Ho: H = 4.8%; H1: µ > 4.8%; right-tailed Ho: H = 4.8%; H1: µ 4.8%; H1: µ = 4.8%; right-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since n is large with unknown o. The Student's t, since we assume that x has a normal distribution with known o. The standard normal, since…
- 32 - The random variable X, which shows the grades of the students in a class in the exam of the statistics course, has a normal distribution with a mean of 80 and a variance of 25. Which of the following is the lowest grade with a probability of 0.3015? a) 32.5 B) 55 NS) 82.5 D) 68 TO) 89Suppose that the random variable z has a standard normal distribution. Sketch each of the following z points, and use the normal table to find each z point. a) z(-0.01)b) z(-0.05)c) z(-0.10)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.)
- Suppose that the random variable z has a standard normal distribution. Sketch each of the following z points, and use the normal table to find each z point. a) z.01 b) z.05 c) z.02Determine whether the following value is a continuous random variable, discrete random variable, or not a random variable. a. The amount of rainfall in a country in a year b. The last book a person in City A read c. The time it takes to drive from City A to City B d. The weight of a hamburger e. The number of people with blood type B in a random sample of 32 people f. The number of home runs in a baseball game a. Is the amount of rainfall in a country in a year a discrete random variable, continuous random variable, or not a random variable? O A. It is a discrete random variable. O B. It is a continuous random variable. O C. It is not a random variable. b. Is the last book a person in City A read a discrete random variable, continuous random variable, or not random variable? O A. It is a discrete random variable. O B. It is a continuous random variable. O C. It is not a random variable. c. Is the time it takes to drive from City A to City Ba discrete randoni variable, continuous random…Suppose the random variable X follows a normal distribution with mean 8 and variance 25. Thus the value of X so that only 20% of all values are above this X is O A. 3.8 O B. None O C. 12.2 O D. 8.3
