please use the number 6 for this question please: A patient is classified as having gestational diabetes if their average glucose level is above 140 milligrams per deciliter (mg/dl) one hour after a sugary drink is ingested. Rebecca's doctor is concerned that she may suffer from gestational diabetes. There is variation both in the actual glucose level and in the blood test that measures the level. Rebecca's measured glucose level one hour after ingesting the sugary drink varies according to the Normal distribution with μ= 140+# mg/dl and σ = #+1 mg/dl, where # is the last digit of your GCU student ID number. Using the Central Limit Theorem, determine the probability of Rebecca being diagnosed with gestational diabetes if her glucose level is measured:Once?#+2 times, where # is the last digit of your student ID?#+4 times, where # is the last digit of your student ID?Comment on the relationship between the probabilities observed in (a), (b), and (c). Explain, using concepts from lecture why this occurs and what it means in context. 2. Suppose next that we have even less knowledge of our patient, and we are only given the accuracy of the blood test and prevalence of the disease in our population. We are told that the blood test is 9# percent reliable, this means that the test will yield an accurate positive result in 9#% of the cases where the disease is actually present. Gestational diabetes affects #+1 percent of the population in our patient’s age group, and that our test has a false positive rate of #+4 percent. Use your knowledge of Bayes’ Theorem and Conditional Probabilities to compute the following quantities based on the information given only in part 2:If 100,000 people take the blood test, how many people would you expect to test positive and actually have gestational diabetes?What is the probability of having the disease given that you test positive?If 100,000 people take the blood test, how many people would you expect to test negative despite actually having gestational diabetes?What is the probability of having the disease given that you tested negative?Comment on what you observe in the above computations. How does the prevalence of the disease affect whether the test can be trusted?3. As we have seen in class, hypothesis testing and confidence intervals are the most common inferential tools used in statistics. Imagine that you have been tasked with designing an experiment to determine reliably if a patient should be diagnosed with diabetes based on their blood test results. Create a short outline of your experiment, including all of the following:A detailed discussion of your experimental design.How is randomization used in your sampling or assignment strategy?The type of inferential test utilized in your experiment.A formal statement of the null and alternative hypothesis for your test.A confidence interval for estimating the parameter in your test.An interpretation of your p-value and confidence interval, including what they mean in context of your experimental design

Question 1A car painting company has determined that the painting time of cars is uniformly distributed between 25 and 105 minutes. What is the probability that it will take between 40 and 65 minutes for that company to paint a car ?Group of answer choices80.75 %42.50 %25.00 %31.25 %Flag this QuestionQuestion 2The waiting times at a certain bus station are uniformly distributed between 7 and 15 minutes. What is the probability of waiting between 9 and 11 minutes ?Group of answer choices0.25080.5000.125Flag this QuestionQuestion 3The cooking time for a dish is uniformly distributed between 10 and 20 minutes. What is the probability that the cooking will take between 14 and 16 minutes ?Group of answer choices0.20000.14160.07500.3146Flag this QuestionQuestion 4A car painting company has determined that the painting time of cars is uniformly distributed between 30 and 105 minutes. What is the probability that this company will take less than 1 hour to paint a car ?Group of answer choices35 %40 %75 %20 %Flag this QuestionQuestion 5The baking time for a cake is uniformly distributed between 10 and 18 minutes. What is the probability that the baking process takes more than 14 minutes ?Group of answer choices80.5000.2500.125Flag this QuestionQuestion 6The driving time for an individual from his home to his office is uniformly distributed between 20 minutes and 1 hour. Compute the probability that this individual takes more than half an hour to drive from home to office.Group of answer choices20 %30 %55 %75 %Flag this QuestionQuestion 7The baking time for a cake is uniformly distributed between 10 and 18 minutes. What is the probability that the baking process takes more than 14 minutes ?Group of answer choices0.5000.2500.1258Flag this QuestionQuestion 8The following graph represents a ____________ distribution.Group of answer choicesnormalbinomialuniformPoissonFlag this QuestionQuestion 9The area under the graph of a ____________ is equal to ____________.Group of answer choiceshistogram ------------ the medianuniform distribution ------------ 1normal distribution ------------ 0scatter plot ------------ 50 %Flag this QuestionQuestion 10The graph of a ____________ distribution has the shape of a rectangle. The graph of a ____________ distribution has the shape of a bell.Group of answer choicesPoisson ------------ uniformnormal ------------ binomialuniform ------------ normalbinomial ------------ uniformFlag this QuestionQuestion 11A) The following graph represents a ____________ probability distribution. B) The following graph represents a ____________ probability distribution. Group of answer choicesA) binomialB) uniformA) normalB) uniformA) uniformB) normalA) discreteB) PoissonFlag this QuestionQuestion 12The ACT scores of students are normally distributed with a mean of 18 and a standard deviation of 6. What percentage of students score between 10 and 15 ?Group of answer choices9.12 %30.85 %78.27 %21.73 %Flag this QuestionQuestion 13The grades of students in an exam are normally distributed with a mean of 75 and a standard deviation of 5. What percentage of grades are between 72 and 90 ?Group of answer choices13.24 %27.56 %72.44 %90.72 %Flag this QuestionQuestion 14A tea bag packing machine manufactures bags of tea whose weights are normally distributed with a mean of 250 g and a standard deviation of 2.5 g. What percentage of tea bags weight less than 245 g ?Group of answer choices45.01 %2.28 %39.26 %97.72 %Flag this QuestionQuestion 15The fuel efficiency of a particular model of car is normally distributed with a mean of 28 miles/gallon and a standard deviation of 2 miles/gallon. What percentage of cars of that model have a fuel efficiency below 25 miles/gallon ?Group of answer choices93.32 %15.87 %6.68 %24.17 %Flag this QuestionQuestion 16Assume that the heights of women are normally distributed with a mean of 65 inches and a standard deviation of 3 inches. If a woman is randomly selected , what is the probability that she is taller than 70 inches ?Group of answer choices0.95220.04780.90440.0956Flag this QuestionQuestion 17The grades of students on a test are normally distributed with a mean of 70 and a standard deviation of 8. What percentage of students scored more than 75 in the test ?Group of answer choices74.02 %23.4 %73.4 %26.6 %Flag this QuestionQuestion 18The Normal Probability Distribution is an example of a ____________ probability distribution.Group of answer choicesdiscretecontinuousPoissonuniformFlag this QuestionQuestion 19The salaries of teachers in a particular school district are normally distributed with a mean of $ 50,000 and a standard deviation of $ 2,500. Due to budget limitations, teachers in the top 2 % of salaries will not get a raise. What is the cutoff salary ( rounded to the nearest dollar ) that separates the teachers that get the raise from those that don't get the raise ?Group of answer choices$ 54,702$ 55,134$ 45,298$ 44,866Flag this QuestionQuestion 20In a cookie factory, the masses of cookies are normally distributed with a mean of 40 g and a standard deviation of 2 g. If the 5 % heaviest cookies are rejected, what is the least weight for a cookie to be rejected ?Group of answer choices43.3 g35.3 g55.7 g41.2 g