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Math 2311 EMCF Homework 4Sections 4.1 – 4.2Honework will NOT be accepted through email or in person. Homework must be submitted throughCourseWare, https://www.casa.uh.edu, before the deadline. Submit this assignment on CourseWare underâEMCFâ and choose ehw4.Problems 1-4 are from section 4.1 #2: Think about a density curve that consists of two straight-line segments.The first goes from the point (0, 1) to the point (0.7, 1) then the second goes from the point (0.7, 1) to thepoint (1.3, 0)1. What is the probability that X falls below 0.5?a.b.c.d.e.0.50.80.30none of these2. What is the probability that X lies between 0.7 and 1.3?a.b.c.d.e.0.50.80.30none of these3. What is the probability that X is equal to 0.5?a.b.c.d.e.0.50.80.30none of these4. What is the probability that X lies above 0.2a.b.c.d.e.0.50.80.30none of these5. Suppose a density curve is defined by the function f (x) = 2.5 for all values between x = 0 to x = 0.4.Find the median of the density curve.a.b.c.d.e.10.22.50.4none of these10.040.00density0.08Use the following to answer questions 6 – 10: The following is the Normal density curve for the MPG of alarge sedan with a mean of 26.5 mpg and standard deviation 3.7.15.419.122.826.530.233.937.66. What approximate proportion of sedans will have a MPG of less than 26.5 mpg?a.b.c.d.e.99.7%95%68%50%none of these above7. What approximate proportion of sedans will have a MPG between 22.8 and 30.2 mpg?a.b.c.d.e.99.7%95%68%50%none of these above8. What is the approximate probability that a sedan will have a MPG less than 19.1 mpg?a.b.c.d.e.0.950.050.0250.50none of these above29. What is the approximate probabiltiy that a sedan will have a MPG between 22.8 and 26.5 mpg?a.b.c.d.e.0.680.340.950.475none of these above10. What is the approximate probability that a sedan will have a MPG between 19.1 and 30.2 mpg?a.b.c.d.e.0.680.950.8150.27none of these above11. The distribution of raw scores on a chemistry final is approximately normal with mean of about 50 andstandard deviation of about 10. What is the probability that a student will have a raw score that ismore than 45?a.b.c.d.e.0.72380.30850.45000.6915none of these12. Which of the following is NOT a property of the Normal distribution?a.b.c.d.e.the area under the Normal density curve must add up to 1the mean is equal to the median, and both lie directly in the middle of the curveapproximately 5% of the data lies OUTSIDE 2 standard deviations from the meanapproximately 68% of the data lies WITHIN 2 standard deviations from the meanall are correct13. A normal density curve has which of the following properties?a.b.c.d.e.It is symmetric.It has a peak centered above its mean.The spread of the curve is proportional to the standard deviation.Only a and ball of these above314. A continuous random variable may assumea.b.c.d.e.any value in an interval or collection of intervalsonly integer values in an interval or collection of intervalsonly fractional values in an interval or collection of intervalsonly the positive integer values in an intervalnone of these15. A description of the distribution of the values of a random variable and their associated probabilities iscalled aa.b.c.d.e.probability distributionrandom variancerandom variableexpected valuenone of these4