Exercise1. In a manufacturing process where glass productsare made, defects or bubbles occur, occasionallyrendering the piece undesirable for marketing. It isknown that, on average, 1 in every 1000 of theseitems produced has one or more bubbles. What isthe probability that a random sample of 8000 willyield fewer than 7 items possessing bubbles?Let n=8000p=0.001

The binomial distribution is a discrete probability distribution in which there are a fixed number…

Answered: Exercise 1. In a manufacturing process…

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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5. If z is a standard normal random variable, find the value of c:P(z < c)= 0.6950 c = _____
2. Let the random variables Y, Y,, ...,Y, be normally distributed with mean 10 and variance 4. Find a valuek such that Σ ;- 10 2
1.The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x1 be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 8880 observations, the sample mean interval was x1 = 63.0 minutes. Let x2 be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 25,691 observations, the sample mean time interval was x2 = 70.2 minutes. Historical data suggest that ?1 = 8.70 minutes and ?2 = 12.48 minutes. Let ?1 be the population mean of x1 and let ?2 be the population mean of x2. (a) Compute a 95% confidence interval for ?1 – ?2. (Use 2 decimal places.) lower limit upper limit (b) Comment on the meaning of the confidence interval in the context of this problem. Does the interval consist of positive numbers only? negative numbers only? a mix of positive and…
4. For a population with a µ = 72 and o = 20. What is the probability of obtaining a sample mean greater than 75 a. for a random sample of N = 100 scores? b. for a random sample of N = 225 scores?
It has been determined that the distribution of faulty products in a factory conforms to Poisson. 2% of the products produced monthly are defective. Calculate the probability of finding 3 defective parts in 250 randomly drawn samples.7a. 0.140b. 0.095c. 0.091D. 0.253to. 0.145
Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail. 16 6 8 9 10 18 14 13 9 10 25 18 13 8 14 3 The sample mean is x = 12.1%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use ? = 0.01. (a) What is the level of significance? Compute the z value of the sample test statistic. (Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
3. Football goal scoring events arrive as a Poisson process in a a 90-minute match at a mean rate of 2.7 goals per match. Find the probability that an interval time is less than 30 minutes: (A) 0.0672 (B) 0.4066 (C) 0.5934 (D) 0.9328
Which of the following random variable follows a continuous distribution? A. The outcome of rolling a die. B. The outcome of flipping a coin C. Next year's demand which is assumed to have 5 possible outcomes. D. A person's hight.
1. A university has 25,000 students, of whom 17,000 are undergraduates. The housing office takes a simple random sample of 500 students; 357 out of the 500 are undergraduates. Fill in the blanks. (If necessary, round using 2 decimal places. For percentages, enter a number between 0 and 1) (a) For the number of undergraduates in the sample, the observed value is _________ but the expected value is ______________ (b) For the percentage of undergraduates in the sample, the observed value is ____________ but the expected value is ____________
Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail. 15 7 7 13 13 20 13 12 5 10 26 22 13 7 11 3 The sample mean is x = 12.3%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use α = 0.01. (a) What is the level of significance? Compute the z value of the sample test statistic. (Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)
5. A coin is selected from a batch of special coins, for which the probability of landing heads is continuously and uniformly distributed between 0.25 and 0.75. Random variable, W, represents the number of tosses until a head is observed. a. Find the expected value of W. b. Find the variance of W.

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