A company launches 15 products, and each of them hasa 40% chance of being profitabile in S years. If each product launch is successful independent of the other launches, what is the probebility thet esactly 7 of the products launch successtullyint independent trials with fived p'of success is a Binomial Distribution A 1253% 17.71 65.23% 21.92
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- (ONE WAY ANOVA) Find the ff: a. mean & variance of each sample b. find the grand mean c. find the between & withinCaptopril is a drug designed to lower systolic blood pressure. In a trial, 12 randomly selected subjects were treated with the drug and another 12 randomly selected subjects were treated with the placebo. Assume the two populations are normally distributed. The results and some summary statistics are shown in the table. Note that some of the summary statistics may not be useful or relevant! Data Group Placebo 200 174 198 170 179 182 193 209 185 155 169 210 (ž1 = 185.3) (s1 = 17.1) Captopril (I2 = 166.8) (s2 = 14.9) d = I1 – 12 (d = 18.6) (sa = 10.1) %3D %3D 191 170 177 167 159 151 176 183 159 145 146 177 9. 4 21 3 20 31 17 26 26 10 23 33 %3D data %3D Using a 0.01 significance level, is there sufficient evidence to support the claim that the mean systolic blood pressure is lower for those treated with the drug than for those treated with the placebo? Use the p-value method. For full marks, include a diagram of the distribution indicating important components of the question.Below is the summary A tutorial school has been running IELTS mock examination for many years. presented by the tutorial school related to the IELTS mock examination in one of the many online classes selected randomly in year 2022. IELTS score in mock examination Number of students <4 5 2 5 7 15 8 10 3 A report presented by this tutorial school 5 years ago indicated that the population mean score of IELTS mock examination was 7.05 points and ihe population proportion of students got 7 points or above was 0.67. (a) Construct a 95% confidence interval estimate of population mean score a student get in the IELTS mock examination in 2022. (b) Test, at 1% level of significance, if the population proportion of students get 7 points or above in 2022 is higher than that in year 2017. (The report must include the (i) null hypothesis and alternative hypothesis, (ii) rejection region(s), (iii) calculation of test statistics, and (iv) conclusion.) (c) If the confidence interval estimate in part…
- The time to complete the Advanced Placement (AP) Statistics Exam in previous years is normally distributed with an average time of 2.4 hours. Because of school closures due to COVID-19, the College Board offered an at-home test for the 2020 AP Statistics Exam. A teacher feels that students, on average, will have a different completion time for the at-home exam. They take a random sample of 25 students that took the exam and their mean time was 2.74 hours with a standard deviation of 0.25 hours. Test to see if the mean time has significantly changed using a 5% level of significance. Give answers to at least 4 decimal places. What are the correct hypotheses? Ho: M H₁: P Based on the hypotheses, find the following: Test Statistic t = Critical-Value t = ± 2.4 #v 2.4 o hours hours5.28 Medical Bills II Consider the medical paymentproblem in Exercise 5.27 in a more realistic setting. Ofall patients admitted to a medical clinic, 30% fail topay their bills and the debts are eventually forgiven. Ifthe clinic treats 2000 different patients over a period of1 year, what is the mean (expected) number of debtsthat have to be forgiven? If x is the number of forgivendebts in the group of 2000 patients, find the varianceand standard deviation of x. What can you say aboutthe probability that x will exceed 700? (HINT: Use thevalues of m and s, along with Tchebysheff’s Theorem,to answer this question.)In a company, the known mean time before the first occupational accident is normally distributed with a mean of 12 years and a variance of 6.76 years². What is the probability that an individual happens to have an accident between 11.3 and 13.6 years of permanence in the company?
- Your company has developed a probability of purchase model based upon the number of promotions to which a customer has been exposed. The dependent variable is the probability that a customer will make a purchase within the following week (0-1). The independent variable is the number of promotions to which the customer has been exposed over the past month.. The model appears as follows: Probability of Purchase = .2 + .075 (# of promotions exposed in past month) Interpret the associated 95% confidence interval if it is .4 - .6. Interpret the associated 95% prediction interval if it is: .35 - .65.In a Block Design experiment, Yasmeen compared the yield of 4 bean cultivars in 3 replications. After analysis of variance, Yasmeen found that Treatment SS (SS)= 362, and Error SS (SS) 765. If t(p<0.05) is assumed 2.06, Calculate the LSD (P<0.05)= decimals ❤ Round up to TwoThe life span of a certain wood cutting machine manufactured by a factory has a normal distribution with a guarantee that any machine that stars malfunctioning within 36 months of the purchase will be replaced by a new one. How many percentages of machines are expected to be replaced in the following cases? Mean of 60 months and variance of 64 months2 Mean of 45 months and variance of 36 months2 Mean of 75 months and variance of 16 months2
- The service times for customers coming through a checkout counter in a retail store are independentrandom variables with mean 1.5 minutes and the variance 1.0. Approximate the probability that 100customers can be served in less than (a) 2 hours (b) 3 hours of total service time.The time to complete the Advanced Placement (AP) Statistics Exam in previous years is normally distributed with an average time of 2.6 hours. Because of school closures due to COVID-19, the College Board offered an at-home test for the 2020 AP Statistics Exam. A teacher feels that students, on average, will have a different completion time for the at-home exam. They take a random sample of 26 students that took the exam and their mean time was 2.73 hours with a standard deviation of 0.25 hours. Test to see if the mean time has significantly changed using a 5% level of significance. Give answers to at least 4 decimal places. What are the correct hypotheses? Ho: Select an answer ✓ H₁: Select an answer ✓ Test Statistic t = ? ✓ Critical-Value t = ± ? ✓ hours Based on the hypotheses, find the following: hours Shade the sampling distribution curve with the correct critical value(s) and shade the critical regions. The arrows can only be dragged to t-scores that are accurate to 1 place after…Are juvenile defendants who are released pending adjudication processed more slowly than those who are detained? The JDCC data set records whether a juvenile was released and the number of months it took for that juvenile’s case to reach a disposition. The sample will be narrowed to black female youth. Released juveniles (Sample 1) had a mean of 4.30 months to disposition (s = 3.86, N = 123) and detained juveniles (Sample 2) had a mean of 3.57 (s = 4.20, N = 64). Using an alpha level of .01, test the hypothesis that released juveniles’ mean time-to-adjudication is significantly greater than detained juveniles’ mean. Assume equal population variances. Use all five steps.
