Question 2a) A box holds 5 red beads and 3 green beads.A bead is taken and not replaced.Three more green beads are added to the box.A second bead is then taken.i) Draw a fully labelled tree diagram.ii) Find the probability that the two beads that are taken from the box areboth green.b)Electric cable is sold in reels. The length of cable on the reels can beassumed to follow a Normal distribution with mean 50 metres and standarddeviation 0.5 metres.11.9% of reels have more than x metres of cable.Find the value of x.

a) A box holds 5 red beads and 3 green beads the total number of beads in box ( first draw) We know…

Answered: Question 2 a) A box holds 5 red beads…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose that in a large class, the instructor announces that the average grade on an exam is 75. Which is more likely to be closer to 75: a.) The exam grade of a randomly selected student in the class? b.) The mean exam grade of a sample of 10 sttudents? Explain.
4. Suppose the incubation period for land turtle eggs is normally distributed with a mean of sixty- seven days and standard deviation 7.4 days. a. Find the probability that a land turtle egg will take at least eighty days to hatch. b. Find the probability that a land turtle egg will take at most fifty-five days to hatch. c. Find the probability that a land turtle egg will take between fifty and eighty-five days to hatch. d. Find the length of time such that 85% of the land turtle eggs will have hatched by then. e. Suppose a veterinarian becomes concerned about the health of the land turtle if it takes longer than ninety days to hatch. What is the probability of this happening if the turtle is healthy? Is it likely for this to happen? f. Find and interpret the 90th percentile.
Assume the weight of groundhogs are approximately normally distributed, with a mean weight of 8.6 pounds, and standard deviation of 1.1 pounds. If you take a random sample of 5 groundhogs, what is the probability the sample mean will be less than 9 pounds? How would you shade the graph representing the scenario above? A) Right-tail including the mean B) Right-tail not including the mean C) Two-tails D) Left-tail including the mean E) Left-tail not including the mean F) Between two-tails OA OB OD OE OF
9. Suppose three fair coins are flipped. Let a random variable count the number of tails. a.) Find the probability distribution. b.) Find the mean of the probability distribution. c.) Find the variance and the standard deviation of the probability distribution.
A population of a certain LGBTQ+ community is consists of 6 measurements 2,3,6,9,11 and 5 2.) What is the variance of the sampling distribution of the sample mean? a.) 4 b.) 3 c.) 2 d.) 1
3. The chance of contacting strep throat when coming into contact with an infected person is estimated as 0.15. Suppose the four children of a family come into contact with an infected person. Design and conduct a simulation to answer the following questions. Begin on Line 115 and conduct 10 trials. a) Estimate the average number of children who will get the disease. b) What is the probability of two of the children getting the disease? c) What is the probability of at least two of the children getting the disease?
48) At a tennis tournament a statistician keeps track of every serve. The statistician reported that the mean serve speed of a particular player was 97 miles per hour (mph) and the standard deviation of the serve speeds was 11 mph. Assume that the statistician also gave us the information that the distribution of the serve speeds was bell shaped. What proportion of the player's serves are expected to be between 119 mph and 130 mph? A) 0.997 B) 0.0235 C) 0.95 D) 0.047
2.) For random variable that counts the number of heads when a coin is flipped four times, find the following: a.) The probability distribution; b.) The probability histogram with breaks=c(-1,0,1,2,3,4).
Solve A) to D)
3) Below is the distribution of 80 graduates with their degree type and average grade. Find the probability that a randomly selected graduate has a B.S. degree, given that the graduate has a B average. ((please check images for accuracy, thank you!!!))
5. Approximately 10% of American high school students drop out of school before graduation. Choose 20 students entering high school at random. Find the probability that a) No more than 10 drop out. b) All stay in school and graduate c) At least 18 graduate. Find the mean and variance of the number of students finished high school and graduated.
A random variable follows a binomial distribution with the probability of success for one trial at 0.83 and 17 randomly selected trials. Round to the fourth. a) Find the mean of the distribution. b) Find the standard deviation of the distribution c) Find the probability of exactly 12 successes. d) Find the probability of exactly 9 successes. e) Find the probability of exactly 7 successes

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