Suppose that in a certain class, grades will be given in a uniform distribution where a = 80, b = 100. Let X be the grade of a randomly-selected student, what is: a. P (X < 90) b. P (X .> 90) c. P (X = 0) d. P (85 < X < 95)
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Suppose that in a certain class, grades will be given in a uniform distribution where a = 80, b = 100. Let X be the grade of a randomly-selected student, what is:
a. P (X < 90)
b. P (X .> 90)
c. P (X = 0)
d. P (85 < X < 95)
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- Suppose that the speed at which cars go on the freeway is normally distributed with mean 71 mph and standard deviation 7 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,)b. If one car is randomly chosen, find the probability that it is traveling more than 67 mph. c. If one of the cars is randomly chosen, find the probability that it is traveling between 74 and 77 mph. d. 83% of all cars travel at least how fast on the freeway? mph.Suppose we want to estimate p, the proportion of undergraduate students who cheat. One strategy to estimate p is to sample n undergraduate students and ask each one the following question directly: Have you ever cheated in answering one of your class requirements (quizzes, exams, assignments, projects, etc.? Let Y₁, Y₂,, Y, denote the "1/0" ("yes/no") responses. a. What is the distribution of Y₁, i=1,2,...,n? b. Based on your answer in (a), find the maximum likelihood estimator of p.Suppose that the speed at which cars go on the freeway is normally distributed with mean 75 mph and standard deviation 9 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,) b. If one car is randomly chosen, find the probability that it is traveling more than 72 mph. c. If one of the cars is randomly chosen, find the probability that it is traveling between 76 and 80 mph. d. 78% of all cars travel at least how fast on the freeway? mph.
- Suppose that the speed at which cars go on the freeway is normally distributed with mean 80 mph and standard deviation 7 miles per hour. Let X be the speed for a randomly selected car. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( 80 | 7 b. If one car is randomly chosen, find the probability that it is traveling more than 79 mph. c. If one of the cars is randomly chosen, find the probability that it is traveling between 82 and 87 mph. d. 71% of all cars travel at least how fast on the freeway? mph. Hint:Suppose that the time spent by children in front of the television set per year has the distribution N(1500, 250) What proportion of children spend less than 1000 hours in front of the television?The graph illustrates the distribution of test scores taken by College Aigebra students. The maximum possible score on the test was 140, while the mean score was 76 and the standard deviation was 14. 34 48 62 76 90 104 Distribution of Test Scores What is the approximate percentage of students who scored between 76 and 90 on the test? What is the approximate percentage of students who scored higher than 104 on the test? What is the appraximate percentage of students who scored higher than 118 on the test? What is the approximate percentage of students who scored between 48 and 104 on the test?
- he mean height of an adult giraffe is 18 feet. Suppose that the distribution is normally distributed with standard deviation 1 feet. Let X be the height of a randomly selected adult giraffe. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,)b. What is the median giraffe height? ft.c. What is the Z-score for a giraffe that is 20 foot tall? d. What is the probability that a randomly selected giraffe will be shorter than 18.2 feet tall? e. What is the probability that a randomly selected giraffe will be between 18.9 and 19.6 feet tall? f. The 70th percentile for the height of giraffes is ft.Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 268 feet and a standard deviation of 45 feet. Let X be the distance in feet for a fly ball.a. What is the distribution of X? X ~ N(,)b. Find the probability that a randomly hit fly ball travels less than 338 feet. Round to 4 decimal places. c. Find the 90th percentile for the distribution of distance of fly balls. Round to 2 decimal places. feetSuppose that the City of Chicago is interested in potential revenues if they introduce a tolling station near O'Hare. Further suppose that the average time between cars is only 3.0 seconds; what is the average value of the distribution?
- Is it possible for the 50th percentile of a distribution to be equal to the 60th percentile? Why or why not? A. No, because you won’t get the same result multiplying by 50 as you do by 60. B. No, because there will always be some values of the distribution in between the 50th and 60th percentiles. C. Yes, this can happen if the distribution is uniform. D. Yes, this can happen if there are many members of the population with the same value.Solve #22 using applications of normal distribution
