The 2010 US National Census provides the following assessment of the number of academic years of graduate education completed by people of 25 years or older.Number of academic years completedNumbers in thousands of people age 25 years or over<1139151026,69931,5094868Expand the table using appropriate functions and calculate the standard deviation of the sample. (5 points)During 2011, the Scottish Crime and Drugs Enforcement Agency (SCDEA) repeatedly seized hauls of illicit white powders in Aberdeenshire. On analysis, these were repeatedly found to contain 2% fentanyl in a mix of 98% lactose. Three out of ten cases also involved other drugs, not just fentanyl.What is the probability of finding only one case of unmixed drugs (only i.e 2% fentanyl mixed in lactose)?What is the probability of finding five cases of unmixed drugs (only i.e 2% fentanyl mixed in lactose)?The probability of three cases having a mix of drugs? (14 points) In an analysis of 15 cases of illicit white powders, calculate the following: The FBI database IAFIS holds records of over 51 million criminal 10-print fingerprint records, each of them theoretically unique. When analyzing fingerprints, there are specific points on each fingerprint that are utilized to distinguish and identify a fingerprint with a database match. Commonly 10 to 12 matching points are used to affect a match, but there is no standard rule to this.On average per month, a particular laboratory uses 15 points to identify and match a fingerprint from a crime scene with a suspect in the database. Calculate the following probabilities:Define in your own words the following terms (5 points):a. Probability.b. Standard normal distribution. c. Continuous Random Variable.Use the z-table to look up the corresponding values for the following tabulated z-score and probability values (7 points):a. z = 2.140b. z = 2.965c. z = - 0.950d. z = - 2.255e. p = 0.1423f. p = 0.99153. The average lethal blood concentration of morphine is estimated to be 2.5 µg/mL with a standard deviation of 0.95 µg/mL. The data is normally distributed. Examine the range of values 0.05 to 4.95 µg/mL. Answer the following questions and provide the appropriate calculations (13 points): a. What is the probability associated with the range lethal morphine blood levels? b. Provide the range of values that lie within 1, 2 and 3 standard deviations from the mean. c. What is the probability that somebody dies if the blood morphine concentration is 0.3 µg/mL.?1.A random sample of 20 observations produced a sample mean of 9.5. Find the critical and observed z-values for each of the following and test each hypothesis at α = 0.05. Write a separate conclusion for each hypothesis. The underlying population standard deviation is known to be 3.5 and the population distribution is normal (5 points):a.H0: µ = 8.75; H1: µ ≠ 8.75b.H0: µ = 8.75; H1: µ > 8.752.Police on a heavily traveled highway claim that the average car exceeds the speed limit of 65 mph by more than 10 mph. A random sample of 50 cars is evaluated and found to have an average speed of 82.5 mph with a standard deviation for this sample of 7.3 mph. Determine the 95% confidence interval for this example, state the null and alternative hypothesis about the police’s claim and determine if the claim is indeed correct at a significance level of α=0.05 (5 points).3.The article entitled “Effect of metformin therapy on 2-h post-glucose insulin levels in patients of polycystic ovarian syndrome” by Saxena et al. discussed the influence of metformin on insulin levels in women with polycystic ovarian syndrome (POCS), http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3017330/?tool=pubmed (Links to an external site.). Summarize the article in terms of the statistics that were used and calculate the following statistics for i) the body mass index, ii) the FSH levels, and iii) the mean hirsutism scores (15 points):a.The 95% and 99% confidence intervals.b.Test the null and alternative hypothesis that the after treatment results are significantly different from the before treatment results.