Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Chapter 6.5, Problem 61E
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At 15:00 it is the end of the school day, and it is assumed that the departure of the students from school can be modelled by a Poisson distribution. On average, 24 students leave the school every minute.
(e) There are 200 days in a school year. Given that Y denotes the number of days in the year that at least 700 students leave before 15:30, find
(ii) P(Y > 150).
Find P(X=4) if X has a Poisson distribution such that 3P(X=1)=P(X=2)
2a) The number of flowers per square meter in Sarah’s garden has a Poisson distribution with mean 0.35. Her garden is covered with 150 square meters of grass. Find lambda λ?
2b) The number of flowers per square meter in Sarah’s garden has a Poisson distribution with mean 0.35. Her garden is covered with 150 square meters of grass. Using Normal approximation, we will need to find the probability that the Sarah’s garden will contain less than 45 flowers. First graph and answer what is the continuity correction?
2c) Using the previous results for lambda and continuity correction,
find z, then graph and use your table to find φ table value of z
Write down your final answer for the probability that Sarah’s garden will contain less than 45 flowers as a decimal number with 4 decimal places.
Chapter 6 Solutions
Mathematical Statistics with Applications
Ch. 6.3 - Let Y be a random variable with probability...Ch. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.3 - The amount of flour used per day by a bakery is a...Ch. 6.3 - Prob. 5ECh. 6.3 - The joint distribution of amount of pollutant...Ch. 6.3 - Suppose that Z has a standard normal distribution....Ch. 6.3 - Assume that Y has a beta distribution with...Ch. 6.3 - Prob. 9ECh. 6.3 - The total time from arrival to completion of...
Ch. 6.3 - Suppose that two electronic components in the...Ch. 6.3 - Prob. 12ECh. 6.3 - If Y1 and Y2 are independent exponential random...Ch. 6.3 - Prob. 14ECh. 6.3 - Prob. 15ECh. 6.3 - Prob. 16ECh. 6.3 - Prob. 17ECh. 6.3 - A member of the Pareto family of distributions...Ch. 6.3 - Prob. 19ECh. 6.3 - Let the random variable Y possess a uniform...Ch. 6.3 - Prob. 21ECh. 6.4 - Prob. 23ECh. 6.4 - In Exercise 6.4, we considered a random variable Y...Ch. 6.4 - Prob. 25ECh. 6.4 - Prob. 26ECh. 6.4 - Prob. 27ECh. 6.4 - Let Y have a uniform (0, 1) distribution. Show...Ch. 6.4 - Prob. 29ECh. 6.4 - A fluctuating electric current I may be considered...Ch. 6.4 - The joint distribution for the length of life of...Ch. 6.4 - Prob. 32ECh. 6.4 - The proportion of impurities in certain ore...Ch. 6.4 - A density function sometimes used by engineers to...Ch. 6.4 - Prob. 35ECh. 6.4 - Refer to Exercise 6.34. Let Y1 and Y2 be...Ch. 6.5 - Let Y1, Y2,, Yn be independent and identically...Ch. 6.5 - Let Y1 and Y2 be independent random variables with...Ch. 6.5 - Prob. 39ECh. 6.5 - Prob. 40ECh. 6.5 - Prob. 41ECh. 6.5 - A type of elevator has a maximum weight capacity...Ch. 6.5 - Prob. 43ECh. 6.5 - Prob. 44ECh. 6.5 - The manager of a construction job needs to figure...Ch. 6.5 - Suppose that Y has a gamma distribution with =...Ch. 6.5 - A random variable Y has a gamma distribution with ...Ch. 6.5 - Prob. 48ECh. 6.5 - Let Y1 be a binomial random variable with n1...Ch. 6.5 - Let Y be a binomial random variable with n trials...Ch. 6.5 - Prob. 51ECh. 6.5 - Prob. 52ECh. 6.5 - Let Y1,Y2,,Yn be independent binomial random...Ch. 6.5 - Prob. 54ECh. 6.5 - Customers arrive at a department store checkout...Ch. 6.5 - The length of time necessary to tune up a car is...Ch. 6.5 - Prob. 57ECh. 6.5 - Prob. 58ECh. 6.5 - Prob. 59ECh. 6.5 - Prob. 60ECh. 6.5 - Prob. 61ECh. 6.5 - Prob. 62ECh. 6.6 - In Example 6.14, Y1 and Y2 were independent...Ch. 6.6 - Refer to Exercise 6.63 and Example 6.14. Suppose...Ch. 6.6 - Prob. 65ECh. 6.6 - Prob. 66ECh. 6.6 - Prob. 67ECh. 6.6 - Prob. 68ECh. 6.6 - Prob. 71ECh. 6 - Let Y1 and Y2 be independent and uniformly...Ch. 6 - As in Exercise 6.72, let Y1 and Y2 be independent...Ch. 6 - Let Y1, Y2,, Yn be independent, uniformly...Ch. 6 - Prob. 75SECh. 6 - Prob. 76SECh. 6 - Prob. 77SECh. 6 - Prob. 78SECh. 6 - Refer to Exercise 6.77. If Y1,Y2,,Yn are...Ch. 6 - Prob. 80SECh. 6 - Let Y1, Y2,, Yn be independent, exponentially...Ch. 6 - Prob. 82SECh. 6 - Prob. 83SECh. 6 - Prob. 84SECh. 6 - Let Y1 and Y2 be independent and uniformly...Ch. 6 - Prob. 86SECh. 6 - Prob. 87SECh. 6 - Prob. 88SECh. 6 - Let Y1, Y2, . . . , Yn denote a random sample from...Ch. 6 - Prob. 90SECh. 6 - Prob. 91SECh. 6 - Prob. 92SECh. 6 - Prob. 93SECh. 6 - Prob. 94SECh. 6 - Prob. 96SECh. 6 - Prob. 97SECh. 6 - Prob. 98SECh. 6 - Prob. 99SECh. 6 - The time until failure of an electronic device has...Ch. 6 - Prob. 101SECh. 6 - Prob. 103SECh. 6 - Prob. 104SECh. 6 - Prob. 105SECh. 6 - Prob. 106SECh. 6 - Prob. 107SECh. 6 - Prob. 108SECh. 6 - Prob. 109SECh. 6 - Prob. 110SECh. 6 - Prob. 111SECh. 6 - Prob. 112SECh. 6 - Prob. 113SECh. 6 - Prob. 114SECh. 6 - Prob. 115SECh. 6 - Prob. 116SE
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- If X has the Poisson distribution with P(X=1) = 2P(X=2), then P(X ≥ 2) is approximately:arrow_forwardFor each of the following assertions, state whether it is a legitimate statistical hypothesis and why:a. $\quad H: \sigma>100$b. $H: \tilde{x}=45$c. $H: s \leq 20$d. $H: \sigma_{1} / \sigma_{2}<1$e. $H: \bar{X}-\bar{Y}=5$f. $H: \lambda \leq 01,$ where $\lambda$ is the parameter of an exponential distribution used to model component lifetimearrow_forwardGiven the specification 90±15, the probability of nonconforming (to the spec) made by a normally distributed process having μ=105, and σ=5 is Select one: a. 0.60 b. 0.45 c. 0.50 d. 0.40 e. 0.55arrow_forward
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- If X1 and X2 constitute a random sample of size n = 2from a Poisson population, show that the mean of thesample is a sufficient estimator of the parameter λ.arrow_forward1a) Derive a maximum-liklihood estimator for the unknown parameter Y 1b) An experienced sales person completes sales following a Poisson distribution, with a mean rate of Y = 1.8 sales/month. A junior sales person completes sales at a mean rate of Y = 0.85 sales per month Find the probability of the joint sales team (experienced and junior) completing exactly 2 sales in any given months, assuming the two sales people act independently of each other. 1c) Find the probability of the joint sales team (experienced and junior) completing more than 2 sales in any given monthsarrow_forwardDerive the formulas for the mean and the varianceof the Poisson distribution by first evaluating E(X) andE[X(X − 1)].arrow_forward
- Consider data 5,1,3,5,5,4,3,2. Poisson distibbution and want to test H0:u=u0 with u0=2. Use wilks theorem to approximate the distribution of -2logA(y) and write the pvalue for testing H0.arrow_forwardA masking tape manufacturer expects 0.04 flaws per meter of tape, on average. The Poisson assumptions hold. Find the probability of exactly 1 flaw in 0.1 meters of tape. 0.0138 0.0289 0.0103 0.0221 0.0040arrow_forwardThe number of staff arrivals at School of Quantitative Sciences between 7.30 a.m. and 9.30 a.m. follows a Poisson distribution with a mean of 16. Find the probability that: a) the number of staff arrivals between 7.30 a.m. and 9.30 a.m. is at least 10. b) the number of staff arrivals between 8.00 a.m. and 8.30 a.m. is at most 5. c) exactly one staff arrives between 8.30 a.m. and 9.30 a.m. Interpret.arrow_forward
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