Large black-tailed gulls usually lay one to three eggs, and rarely have a fourth egg clutch. Itis thought that clutch sizes are limited by how effectively parents can incubate their eggs.Suppose that on average, gulls have a 10% of laying 1 egg, 17.9% of laying 2 eggs, 20.3%chance of laying 3 eggs, and 51.8% chance of laying 4 eggs. What is the expected value ofthe number of eggs laid by a random sample of 100 gulls? Round your answer to five decimalplaces.

Let's denote the number of eggs laid as X, and the probabilities as follows:We are asked to find the…

Answered: Large black-tailed gulls usually lay…

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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A small river is found to be polluted due to the chemical waste from two major industries, A and B. Due to the strict standards enforced by the EPA, the probability of controlling the pollutions from A and B are 0.7 and 0.85, respectively, in the next two years. It is estimated that, if only one of the industries complies with the strict standards of EPA, there is a 75 percent probability of controlling the pollution in the river to an acceptable level. (a) Find the probability of controlling the pollution in the river in the next two years. (b) If the pollution in the river is not controlled in the next two years, what is the probability that it is caused entirely by industry A?
A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 51 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 5000 aspirin tablets actually has a 5% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
A pair of dice is rolled, and the larger of the two numbers showing is recorded. Find the expected value of this experiment.
A kissed frog has a 70% chance of turning into a prince, while a kissed toad has only a 20% chance of turning into a prince. If 16 frogs and 18 toads are kissed, what is the expected number of princes produced?
The M&M/Mars candy company does a lot of market research to determine the most appealing mix of colors in M&M candies. Recently, one mix was: Purple 20%; Yellow 20%; Red 20%; Orange 10%; Green 10%; Blue 10% and Brown 10%. Suppose you reach into a bag of M&M candies and draw out ONE candy at random. What is the likelihood of drawing a Purple candy?
Let (X, Y ) be independent and uniformly distributed random variables (RVs) on the interval[0, 1]. Equivalently, let (X, Y ) be a point chosen uniformly at random in the unit box [0, 1] × [0, 1] on the(x, y) plane. Define the RV Z ≜ √X^2−Y^2 as the random distance of the point (X, Y ) from the origin (0, 0). Find the probability density function (PDF) for the RV Z.
A small business is studying the number of customers that enter the store. They record the number of customers entering every hour for three days, and find that 27% of the time two customers enter the store in an hour, 28% of the time of the time one customer enters the store in an hour, and the remainder of the time no one enters the store in an hour. What is the expected number of customers per hour?
In a multinational company, a server is installed to handle 200 computers. There is 40% chances that the sever is failed to perform certain task. What is the probability at least 3 out of 10 randomly selected servers will perform their tasked properly.
A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 47 tablets, then accept the whole batch if there is only one or none that doesn't meet the required specifications. If one shipment of 6000 aspirin tablets actually has a 3% rate of defects, what is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected? The probability that this whole shipment will be accepted is (Round to four decimal places as needed.)
A gas station has three grades of fuel, regular, premium and diesel. Due to problems with the supply chain, the probabilities that the station will run out of any three fuel types in a week are 0.10, 0.16 and 0.24, respectively. These probabilities are statistically independent. Also, if there is a shortage of diesel, the probability of a shortage of premium becomes 0.25. 1. How likely is the station to run out of all three fuels in a given week? 2. What is the probability that if regular runs out, both premium and diesel will also run out? 3. What is the probability that the station will run out of at least one of either premium and diesel? 4. What is the probability that the station will run out of at least 2 of the fuels in a week?
A railroad between Fairbanks and the Brooks Range in Alaska will have a most likely construction cost of $932,699 per kilometer. If there is more permafrost than estimated (a probability of 0.3), then the cost will increase by 40%. If there is less permafrost than estimated (a probability of 0.2), then the cost will decrease by 25%. What is the expected value for the first cost per kilometer
A manufacturer wishes to estimate the accuracy of its final visual inspection process. A random sample of 180 devices is selected from production. An item is defective or “bad” if it contains at least one visually noticeable cosmetic defect. The process improvement team agrees that the sample contains 27 bad items and 153 good items. The team gives the items to a “certified” operator for inspection. The operator rejects 10 good pieces and accepts 11 bad pieces and classifies the remainder correctly. What is the probability that the inspector will reject an item? P(inspector will reject an item) = ________%. Enter value using one decimal place.

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