4-42. For X~ N(32, 72), find two values x, and X2, symmetrically lying on each side of the mean, with P(x, < X< x,) = 0.99. %3D
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- Assume that the entire sample has 8 positive observations and 4 negatives observations. Variable X1: at the left branch has 9 positive observations and 3 negatives observations;at the right branch has 8 positive observations and 8 negative observations. What is the information gain or reduction in uncertainty of X1 using the Gini index? (round to two decimal spaces)Gjcv1 (a) Discuss the two expressions -x;- )² and E(x;- )², both of which are used (n-1) i=1 to measure the spread of a set of observations x1, x2, . .., X. (b) A random sample of n observations is taken from a distribution; the sum of the observations is t, and the sum of the squares of the observations is 12. Explain how to estimate the mean and the variance of the distribution from which the random sample was taken. (c) Given the random sample described in part (b), write down expressions (based on 11 and t2) for estimates of the mean and variance of the mean of a further, independent, random sample of size m , from the original distribution. (d) Given that n = 25, 1, = 400 and t2 = 8800, construct a 99% confidence interval for the mean of the distribution, and use it to test whether or not this mean could be 20.
- Q2. A laundry for car wash found that the average, for small size car, cleaning time is 5 mins in the morning and 6.5 mins at evening time when a sample of size 30 is taken at the two time periods. From the previous record, the laundry manager knew that car oj = 2 mins for the morning shift and oz = 2.5 mins for morning and evening repectively. Find the interval estimate for 4 - 42 with 90% confidence level.Here is part of a calculation in a spreadsheet working with population data of x. Which statement is incorrect? Q4. frequency,f 3 5 4 2 7 Total 10 23 ΣΤ= 10 & Σx = 23 & Σίx 49 E(x) = 4.9 The median of x is (4 + 7)/2. А. В. %3D C. D. H = 4.9 O A. A В. В С. С O D. DBelow is the frequency distribution showing the result of an IQ test of a group of| students in a certain college. Copy the table and fill all the columns for each category. CI [x - X] fQuick!X ~ N(60, 14). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let ΣX be the random variable of sums.Give the distribution of X. Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.) P(X < 60) =.Find the 30th percentile.P(-0.34Complete the table with the assumption that the mean falls on the 75-79 intervalA large automobile insurance company selected samples of single and married male policyholders and recorded the number who made an insurance claim over the preceding three-year period. Single Policyholders Married Policyholders 721 = 575 n2 = 740 Number making claims = 115 Number making claims = 111 a. Use α = 0.05. Test to determine whether the claim rates differ between single and married male policyholders. z-value p-value We can conclude (to 2 decimals) X (to 4 decimals) that there is the difference between claim rates. b. Provide a 95% confidence interval (to 4 decimals) for the difference between the proportions for the two populations. Enter negative answer as negative number.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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