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. Σx = 63.8; Σx2 = 520.96; Σy = 89.8; Σy2 = 1046.96; Σxy = 731.35 x 6.2 8.7 7.0 7.5 8.1 6.9 10.0 9.4 y 9.7 10.8 10.5 11.3 14.2 7.0 14.1 12.2 (a) Find the equation of the least-squares line. (Round your answers to three decimal places.) ŷ = + x (c) Find the sample correlation coefficient r and the sample coefficient of determination r2. (Round your answers to three decimal places.) r =   r2 =   Explain the meaning of r2 in the context of the application. (Round your answer to one decimal place.) % of the variance in blood glucose leve

The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)

The undergraduate grade point averages​ (UGPA) of students taking an admissions test in a recent year can be approximated by a normal​ distribution, as shown in the figure.   ​(a) What is the minimum UGPA that would still place a student in the top 10​% of​ UGPAs? ​(b) Between what two values does the middle 50​% of the UGPAs​ lie?               3.4042.8Grade point average μ=3.40 σ=0.17 x         A normal curve labeled mu = 3.40 and sigma = 0.17 is over a horizontal x-axis labeled Grade point average from 2.8 to 4 in increments of 0.3 and is centered on 3.40.       ​(a) The minimum UGPA that would still place a student in the top 10​% of UGPAs is nothing. ​(Round to two decimal places as​ needed.) ​(b) The middle 50​% of UGPAs lies between nothing on the low end and nothing on the high end. ​(Round to two decimal places as​ needed.)

Assume two normal distributions where μ1 = 0.0001, σ1 = 0.01, μ2 = -.0002, σ2 = 0.015, and ρ = .45. Using zs = { .814, .259 }, generate z1 and z2.

Let L be the random variable for the length of time, in years, that a person will remember an actuarial statistic. For a certain popula- tion, L is exponentially distributed with mean 1/Y, where Y has a gamma distribution with a = 4.5 and 3 = 4. Find the variance of L.

The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x1 be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 9520 observations, the sample mean interval was x1 = 62.8 minutes. Let x2 be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 23,117 observations, the sample mean time interval was x2 = 73.0 minutes. Historical data suggest that ?1 = 8.98 minutes and ?2 = 12.83 minutes. Let ?1 be the population mean of x1 and let ?2 be the population mean of x2. (a) Compute a 90% confidence interval for ?1 – ?2. (Use 2 decimal places.) lower limit       upper limit       (b) Comment on the meaning of the confidence interval in the context of this problem. Does the interval consist of positive numbers only? negative numbers only? a mix of positive and…

Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal, For the population of healthy female adults, suppose the mean of the x distribution is about 4.64, Suppose that a female patient has taken six laboratory blod tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9 4.2 4.5 4.1 4.4 4.3 () Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) C) Do the given data indicate that the pooulation mean RBC count for this patient is lower than 4.647 Use a- 0.05. (a) What is the level of significance? State the nul and alternate hypotheses. O Hn: 4- 4.64; H: 4.64 O Ho: H> 4.64; H:u- 4.64 O Hn: H- 4.64; H: H 4.64 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal,…

Question 5 Find the 65 -th percentile for a normal random variable X~ N(μ= 36.1,0 = 5.4). The 65-th percentile for X is (Round the answer to 2 decimal places)

Let the random variable x have a normal distribution with a mean value of 70 and a variance of 25. Then find the probability that P(x < 80).