Consider a population of the fruitfly Drosophila melanogaster in which 30% of the individuals areblack because of a mutation, while 70% of the individuals have normal gray body color. Supposethree flies are chosen at random from the population; let Y denote the number of black flies outof the three. Then the probability distribution for Y is given by the following table:(a) P(Y ≥2)(b) P(Y ≤2)Y (No. Black) Probability0.3430.4410.1890.0271.0000123Total

The question is about discrete probability distribution.Given :

Answered: Consider a population of the fruitfly…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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When the health department tested private wells in a county for two impurities commonly found in drinking water, it found that 10% of the wells had neither impurity, 90% had impurity A, and 20% had impurity B. (Obviously, some had both impurities.) If a well is randomly chosen from those in the county, find the probability distribution for Y, the number of impurities found in the well. P(no impurities)= P(exactly one impurity)= P(both impurities)=
Consider a large ferry that can accommodate cars and buses. The toll for cars is $3, and the toll for buses is $10. Let x and y denote the number of cars and buses, respectively, carried on a single trip. Cars and buses are accommodated on different levels of the ferry, so the number of buses accommodated on any trip is independent of the number of cars on the trip. Suppose that x and y have the probability distributions shown below. x 0 1 2 3 4 5 p(x) 0.03 0.09 0.23 0.37 0.19 0.09 y 0 1 2 p(y) 0.55 0.10 0.35 (a) Calculate the mean of x. Calculate the standard deviation of x. (Round the answers to three decimal places.) (b) Calculate the mean of y. Calculate the standard deviation of y. (Round the answers to three decimal places.)
Given the new fad of health consciousness, a random sample of 400 college students was asked what their preferred type of drink was and whether they took regular or sugar free. The following table gives a two-way classification of the responses. Regular Sugar free TOTALS Juice 210 95 305 Iced Coffee 75 20 95 TOTALS 285 115 400 (a) If one student is selected at random from these 400 students, find the probability that this student (i) Prefers sugar free drinks (ii) Prefers juice (iii) Prefers regular juice (iv) Prefers juice given that it is a sugar free drink. (v) Prefers iced coffee or that drinks must be sugar free. (b) Are the events 'prefers juice' and 'prefers sugar free drinks' independent? Use probabilities to state your answer.
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2. The number of patients visiting an emergency room during the graveyard shift (11:00pm-7:00pm), denoted by the random variable X, has the following probability distribution: 1 2 3 4 5 P(X=x) .05 .20 .25 .20 .10 .15 .05 a. Find the probability there will be 3 or more emergency room patients during a randomly selected 8-hour graveyard shift. b. Find the probability there will be an even number of patients. c. Find the probability there will be at least 2 but not more than 5 patients. d. Find the probability there will be less than 2 patients. e. How do you suppose the probability distribution above was obtained?
A company that sells binders decides to run a promotion on their 1-inch and 2-inch size binders. Theydiscount the 1-inch binders to $1 per binder and discount the 2-inch binders to $2 per binder. They limitsales to a quantity of 5 of each size of binder per customer. The probability distribution of “X = the numberof 1-inch binders purchased by a single customer during the promotion period” is given in the table below. X 1 2 3 4 5 P(X) 0.02 0.09 0.12 0.15 0.62 a) Compute the mean and standard deviation of X. b) The company’s cost of manufacturing a single 1-inch binder is $0.25. What is the expected profit (indollars) that the company will make, per customer, for 1-inch binder sales during the promotion? c) The mean and standard deviation of “Y = the number of 2-inch binders purchased by a singlecustomer” is 2.74 and 1.25, respectively. Assume that the number of 1-inch and 2-inch binderspurchased are independent random variables. What are the mean and standard deviation of the…
1.A family wishes to adopt 4 pets from a total of 13 dogs and 7 cats available at an animal shelter. The variable "x" being measured is the number of dogs. Show the probability distribution table, using 3 columns: one for x, one for P(x), and one for x*P(x). The second column should show calculations using C(Dt). 2. A student forum at a high school needs to elect 5 people from 10 Grade 11 students and 15 Grade 12 students who are available. The variable"" being measured is the number of Grade 12 students. Show the probability distribution table, using 3 columns: one for x, one for P(x), and one for x*P(x). The second column should show calculations involving C(Dt).
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Q.7 A physical therapist at Enormous State University knows that the football team will play 40 percent of its games on artificial turf on this season. He also knows that a football player's chance of incurring a knce injury are 30 percent higher if he is playing un artificial tof instead of grans. If a player's probability of knee injury on artificial turf is 0.42, what is the probability that (a) A randomly selected football player inom aknee injury! (b) A randomly selected football player with a knee ingay incurred the injury playing on grasa?
A car dealer is trying to sell five used cars. She attempts to sell a car to each customer that walks in. Suppose that only 7% of all the potential customers are willing and able to purchase a car, and assume that each customer acts independently of one another. Let X denote the number of customers that walk in before all five cars are sold. What is the distribution of X? What is the probability that the last car is sold to the 100th customer?

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