If two points are selected on a straight line of length a units at random, find the probability that none of the three line segments generated by the two random points a has length less than
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- A random point is chosen inside a triangle with height h and base lenght b. what is the expected value of the perpendicular distance of the point to the base?A surface has infinite parallel lines at distance d from adjacent lines. We have a needle of length l which we throw randomly on the surface. What is the probability that the needle intersects a line? Assume l < d.3) A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed with mean 200 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first bulb replacement. Let Xi, i = 1, . . . , 5, be the lifetimes of the five bulbs. Assume the lifetimes of the bulbs are independent.
- In rolling a fair die once, what is theprobability of rolling a 2 or an oddnumber? show solutionIf a point randomly located in an interval (a,b) and if y denotes the location of the point, then y is assumed to have a uniform distribution over (a,b). A plant efficiency expert randomly selects a location along 500-ft assembly line from which to observe the work habits of the workers on the line. What is the probability that the point she selects is a). within 25 feet of the end of the line? b.) within 25 feet of the beginning line? c.) closer to the beginning of the line than to the end of the line?Assume that females have pulse rates that are normally distributed with a mean of μ=76.0 beats per minute and a standard deviation of σ=12.5 beats per minute. Complete part a through c a) If 1 adult female is randomly selected. Find the probability that her pulse rate is less than 82 beats per minute (Round to four decimal places as needed) b) If 4 adult females are randomly selected, find the probability that they have a pulse rates with a mean less than 82 beats per minute (Round to four decimal places as needed) c) Why can the normal distribution be used in part (b) even though the sample size don't exceed 30?(options are the image below)
- Consider a set of data (x;, y;), i = 1,2, .,n and an intercept model given by: 1. Yi = Bo + Ei with E(s;) = 0, Var(ɛ;) = o? and all ɛ,'s are independent and normally distributed. Derive the standard error of the point estimator Bo.If the roots of the quadratic equation x – ax + b = 0 are real and b is positive but otherwise unknown, what are the expected values of the roots of the equation. Assume that b has a uniform distribution in the permissible range. -Utilize this spreadsheet ✓. a) Use the COUNTIFS function to get the percentage of values in "Category" (column C) that say "Rush". Give answer to 4 decimal points. The answer is b) Use the percentage from part a to get the probability that from a random sample of 100 Category values, that between 30 and 35 would be Rush. Give answer to 4 decimal points.
- If a path of length 10 is randomly selected between point O(0,0) and point A(4,6), and movement is restricted to only travel along line segments connecting points with integer coordinates and parallel to the coordinate axes, calculate the probability that the path will intersect point B(1,2).Eht///55BJPRC4rQHWKawiv2z PlohPZXNnCn4sJc6i79t9nMQ/edit $ scholarships Request 1) Marketing: Income What is the income distribution of super shoppers. In the following table, income units are given in thousands of dollars, and each interval goes up to but does not include the given high value. The midpoints are given to the nearest thousand dollars Income 5-15 15-25 25-35 35-45 45-55 55 and range more Midpoint, x 10 20 30 40 50 60 Percent of 21% 14% 22% 15% 20% 8% super shoppers a) Using the income midpoints, x and the percentage of super shoppers, do we have a valid probability distribution? Explain. b) Use a histogram to graph the probability distribution of part (a) c) Compute the expected incomepu of a super shopper. d) Compute the standard deviation o for the income of super shoppers. 2)The director of a health club conducted a survey and found that 23% of members used only the pool for workouts. Based on this information, what is the probability that, for a random sample of 10…Q3) The table below show the number of hours(x) 20 students spent studying spansh in the month before an examination and their percentage score(y). A) Determine SEE If you have the model y = 0.5x +49 B)Find the fit line ( Regrsion line) for these points Hours of study (x) Exam mark%(y) 22 70 21 13 33 25 32 40 15 26 27 18 19 10 21 44 46 17 28 19 20 62 90 58 78 80 66 56 62 68 50 74 76 57 69 58 64 dakhee