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- Suppose that arrival times at a certain emergency care center are following a Poisson process with a mean rate of λ = 0.2 arrivals per minute. Let T be the time until the third arrival. Find the mean and the variance of T, and find P(T ≤ 10) to four decimal places. Part 1 out of 3The mean of T is _______minutes.X is a discrete random variable with the following PMF: • P(X = 5.5) = 0.25 • P(X = -2.5) = 0.25 P(X = 8) = 0.5 Find the standard deviation of X.Let X denote the sample average for a random sample with mean uu and variance 02. Consider the following estimator for u: W=n+2/n+1°X Is W as consistent estimator of u? a. Yes b. No c. It depends
- 2.2. Let Y₁, Y₂Yn denote a random sample from a gamma distribution with each Y-gamma (0; B) with known. Find a sufficient statistic for 8.The following data represent a random sample of 5 observations. Assume that Y is a linear function of X and a normally distributed disturbance term with a mean of zero and a constant variance. In other words: Y = a + bX + u, u ~ Observation Y X 1. 1 17 2. 3 13 3. 5 8 4. 7 10 5. 9 2 Create a scatterplot of this dataset (either manually, or by using Excel graphing functions) Calculate the sample means, variances, and standard deviations of the variables X and Y either “by hand” or by using Excel and write one sentence describing what each of these mean in terms of the dataset. The calculations below should be done by applying the bivariate regression formulas. In other words, do them “by hand” using a calculator or in Excel in a manner that I can clearly see the formulas you have used. You should also check your calculations by entering the data into an Excel sheet and using the regression analysis function under Data Tools.…The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 11.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight full-time faculty for one week is shown in the table below. At a = 0.01, can you reject the dean's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 12.1 8.9 11.8 8.4 7.2 10.1 12.1 8.7
- A random sample of 160 car crashes are selected and categorized by age. The results are listed below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39% for the 26-45 group, 31% for the 45-65 group, and 12% for the group over 65. Calculate the chi-square test statistic χ2 to test the claim that all ages have crash rates proportional to their driving rates. Age Under 26 26 – 45 46 – 65 Over 65 Drivers 66 39 25 30Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(e 14-25. A car hire firm has two cars which it hires out day by day. The number of demands for a car on each day is distributed as a Poisson variate with mean 1-5. Calculate the proportion of days on which (i) Neither car is used (ii) Some demand is refused.Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(Let x be a random variable that represents blood glucose level after a 12-hour fast. Let y be a random variable representing blood glucose level 1 hour after drinking sugar water (after the 12-hour fast). Units are in milligrams per 10 milliliters (mg/10 ml). A random sample of eight adults gave the following information. Σχ - 64.2; Σ ? = 528.24; Ey = 90.4; Ey² = 1063.88; Exy = 741.77 6.2 8.6 7.0 7.5 8.3 6.9 10.0 9.7 y 9.7 10.3 10.9 11.5 14.2 7.0 14.6 12.2 Find the equation of the least-squares line. (Round your answers to three decimal places.) Find the sample correlation coefficient r and the sample coefficient of determination r. (Round your answers to three decimal places.) r = 2 = If x = 7.0, use the least-squares line to predict y. (Round your answer to two decimal places.) y = Find an 80% confidence interval for your prediction. (Round your answers to two decimal places.) lower limit mg/10 ml upper limit mg/10 ml Use level of significance 1% and test the claim that the…A random sample of size 10 yielded roughly "mound-shaped" data with a sample mean of 63.5 and a sample variance of 60.8. Let (L, OU) be the interval estimate that contains the population mean with 95% probability. Find the width of the interval. That is, find 0 – 0₁. 4.52 5.49 5.58 5.70 9.04 10.99 11.16 11.40 none of the other answers give the correct widthRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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