Dandelions are studied for their effects on crop production and lawn growth. In one region, the mean number of dandelions per square meterwas found to be 5.0. Use the Poisson distribution to find the indicated probabilities.a. Find the probability of 8 dandelions in an area of 1 m².b. Find the probability of at least 8 dandelions in an area of 1 m.?.c. Find the probability of at most 9 dandelions in an area of 1 ma. The probability of 8 dandelions is.(Round to four decimal places as needed.)

Given that X~Poisson(λ=5) Probability mass function of X is P(X=x)=λxe-λ/x! , x=0,1,2,___

Answered: Dandelions are studied for their…

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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The number of paint blisters produced by an automated plating process is Poisson distributed with a rate of 0.06 blisters per square meter. The process is about to be used to paint an item that measures 5 by 12m. what is the probability that the finished surface will have a. No blisters at all? b. Between five and eight blisters, inclusive? c. More than 2 blisters?
Suppose that the speed at which cars go on the freeway is normally distributed with mean 78 mph and standard deviation 9 miles per hour. Let X be the speed for a randomly selected car. a. What is the distribution of X? X N( b. If one car is randomly chosen, find the probability that it is traveling more than 75 mph. Round to 4 decumal places. c. If one of the cars is randomly chosen, find the probability that it is traveling between 81 and 87 mph. Round to 4 decimal places.
According to a recent survey, 78% of web users share their password with others. Consider a random selection of 45 users and denote the proportion of them sharing their password as p. a. Calculate the mean and the standard error for p. b. Describe the sampling distribution of p and draw a graph of this probability distribution with its mean and standard deviation. c. What is the probability that less than 90% of them are sharing their password with others? d. What is the probability that more than 60% of them are sharing their password with others?
Suppose that the speed at which cars go on the freeway is normally distributed with mean 80 mph and standard deviation 10 miles per hour. Let X be the speed for a randomly selected car. a. What is the distribution of X? X - N( b. If one car is randomly chosen, find the probability that it is traveling more than 79 mph. Round to 4 decumal places. c. If one of the cars is randomly chosen, find the probability that it is traveling between 83 and 86 mph. Round to 4 decimal places.
Sixty-two percent of seniors attend a particular school in a school district. Assume 500 seniors within this school district are sampled. a. Can this distribution be approximated using the Normal model? Explain. b. Use the Normal approximation to estimate the probability that at least 290 senior students are enrolled at this particular school. c. Use the Normal model to estimate the probability that between 200 and 300 senior students who are sampled are enrolled at this particular school.
e) Suppose that weekly household expenditures on petrol are normally distributed, with a mean of $120 and a standard deviation of $50. i. A family is randomly selected. Find the probability that this family spends more than $245 per week on petrol? A 2.5 B 0.0062 C 0.9938 D 0.0202 ii. The government wants to promote public transport and will award a prize to the families who spend the lowest amount on petrol. If the government only wants to give a prize to 10% of households, what is the most that a family is allowed to spend on petrol each week to obtain the prize? A $56 B $184 C $3.50 D $217.60 In a sample of 25 families, what is the probability that the average weekly expenditure on petrol will be less than $105? ii. A 0.0668 B 0.9332 C 0.3821 D 0.6179
The number of accidents that occur at a busy intersection is Poisson distributed with a mean of 4.4 per week. Find the probability of the following events. A. No accidents occur in one week. Probability = B. 7 or more accidents occur in a week. Probability = C. One accident occurs today. Probability =
In a given company, employee should sign in using the biometric time clock. There are 3 devices in thecompany and the probability that it works is 95%.Let x be the random variable of the number of devices working at a given day.1. Construct the probability distribution of x.2. Find the mean value and interpret it.3. Find the standard deviation and interpret it.

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