A random right triangle can be constructed as follows. Let X be a random angle whose distribution is uniform (0, 7/2) i.e X Unif(7/2) and b be a random base whose distribution is uniform (0, 1) i.e. b Unif(1). Here X and b are independent. For each X and b, construct a triangle with base b and angle X. Here Y height of the random triangle. Find the probability density function of height Y. %3D

Let X have a uniform on the interval (4, 9). Find the probability that the sum of 2 independent observations of X is greater than 16.

can you solve this for me by showing step by step for each question? Acme Food manufactures and sells bags of doughnuts whose weights follow a normal distribution with a mean of 400g and standard deviation 8g. a) Find the probability that a bag of doughnuts weights less than 410g  b) Find  P (X>412) c) Find P (395 < X < 404) d) The company can be prosecuted if the bags are less than 380g, if the company sells 50 bags per day find the expected number of bags under this weight.  e) On a typical day 1.22% of bags are rejected as they are too heavy. Find the rejection weight.

Please draw bell shape diagram with shaded area for both a and b.

If 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?

find PLAoreore) for ethe guilenpélebin pCA=032 ;P(B) =0:29, e(6) s012 , a -D0:12. (A and B) =0.12;PCA and C)=0-02 prBand C) PCA and B and Ĉ = O.01 pA or B or c = =0.06. %3D

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)

This dot plot (burglary rates per 100,000 persons in 350 U.S. cities) shows a distribution that is skewed to the left (negatively skewed). 200 400 600 S00 1000 1200 1400 1600 1800 2000 2200 Buglary True or False True False < Prev 6 of 19 Next arch 22

When we attempt to locate a target in two-dimensional space, suppose that the coordinate errors are independent normal random variables with mean 0 and standard deviation 2. Find the probability that the distance between the point chosen and the target exceeds 3.

The screen of a navigational radar station represents a circle of radius a. As a result of noise, a spot may appear with its center at any point of the circle. Find the expectation and variance of the distance between the center of the spot and the center of the circle.