4. A geologist has collected 10 specimens of basaltic rock and 10 specimens of granite.The geologist instructs a laboratory assistant to randomly select 15 of the specimensfor analysis.a. What is the probability mass function of the number of granite specimensselected for analysis?b. What is the probability that all specimens of one of the two types of rock areselected for analysis?c. What is the probability that the number of granite specimens selected foranalysis is within 1 standard deviation of its mean value?

Answered: Image /qna-images/answer/602fbbb0-1ee4-4ce3-945a-4664f137d0b4.jpg

Answered: 4. A geologist has collected 10…

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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1. A 100-watt light bulb has an average brightness of 1640 lumens, with a standard deviation of 62 lumens. a. What is the probability that a 100-watt light bulb will have a brightness more than 1800 lumens? b. What is the probability that a 100-watt light bulb will h than 1550 lumens? c. What is the probability that a 100-watt light bulb will have a brightness between 1600 and 1700 lumens?
A production line in a factory, assembles laptops. A random sample of assembly time of 36 laptops has been drawn from this factory. Suppose, the population distribution has a mean assembly time of 25 minutes and standard deviation 6 minutes. What is the probability that a sample mean is more than 27 minutes?r Select one: a. =P(Z>2) O b. None of the others c. =P(Z>27) O d. =P(Z<2) %3D e. =P(Z<6)
2. Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let X be the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let X be the random variable representing the mean time to complete the 16 reviews. Assume that the 16 reviews represent a random set of reviews.Find the probability that the mean of a month's reviews will take Yoonie from 3.5 to 4.25 hrs. Give the probability statement and the probability. (Enter exact numbers as integers, fractions, or decimals for the probability statement. Round the probability to four decimal places.)
An online retailer operates two independent warehouses (A & B) where it keeps its inventory. Each warehouse has a .05 probability of experiencing a fire. If a fire is experienced in a given warehouse, $1,000 in inventory will be lost. What is the pooled standard deviation of the warehouses per warehouse (round to the nearest whole number)?
An automated machine in a manufacturing process is operating properly if the length of animportant component is normally distributed, with mean = 117 cm and std. dev = 5.2 cm. Find the probability that, if four units are randomly selected, their mean length is greaterthan 120 cm.
Assume that the heights of 6000 male students at a university are normally distributed with mean 64.0 inches and standard deviation 2.7 inches. If a random sample of 81 students are selected with replacement, What is the probability that the average height in the sample will be between 63.34 and 64.45 inches? O A. 0.849 O B. 0.9193 O C. 0.6803 O D. 0.7767
10. Bags of grain in a warehouse have a mean weight of 60 pounds with a standard deviation of 4 pounds. a. In random samples of 36 bags, what is the probability the total weight of the bags is less than 2100 lb? b. In random samples of 36 bags, what is the 80th percentile for the total weight of the 36 bags?
A farmer harvests several heads of iceberg lettuce. The weight of the heads of lettuce are normally distributed with a mean weight of 2.2 pounds and a standard deviation of .55 pounds. If you choose a head of lettuce at random, what is the probability that the head you chose will weigh: a) Less than 2 pounds? b) Greater than 2.5 pounds? c) Between 1.8 pounds and 2.7 pounds?
Three items are drawn in randomly from a population of 7 items. The item drawn may be defective or non-defective. Random variable is the occurrence of non-defective items. Total defective items in the population are two. Required: 1. Make a frequency distribution table of the random variable. 2. Find the expected value of non-defective items in the random experiment.
6. A tennis player makes a successful first serve 60% of the time. Assume that each serve is independent of the others. If the player serves 8 times, what is the probability that she gets exactly 3 successful first serves? A. 0.0065 B. 0.216 C. 0.124 D. 1.298 7. A researcher reported that the mean weekly television viewing time for children aged 2-11 years is 24.5 hours with a standard deviation of 6.2 hours. Assuming that the weekly television viewing times are unimodal and symmetric (i.e., approximately bell-shaped), 99.7% of all such children are expected to watch between what range of hours of TV per week? Provide a lower and an upper bound. A. 5.9 and 43.1 B. 18.3 and 30.7 C. 12.1 and 36.9 D. 12.1 and 24.5 8. The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percent of pencils will have a diameter greater than 0.328 inches. A. 0.9974
The average number of acres burned by forest and range fires in a large county is 3,900 acres per year, with a standard deviation of 550 acres. The distribution of the number of acres burned is normal. a. Compute the probability that more than 4,000 acres will be burned in any year. b. Determine the probability that fewer than 3,000 acres will be burned in any year. C. What is the probability that between 1,500 and 3,500 acres will be burned? d. In those years when more than 4,500 acres are burned, help is needed from eastern-region fire teams. Determine the probability help will be needed in any year. a. The probability that more than 4,000 acres will be burned is (Round to four decimal places as needed.) b. The probability that fewer than 3,000 acres will be burned is (Round to four decimal places as needed.) c. The probability that between 1,500 and 3,500 acres will be burned is (Round to four decimal places as needed.) d. The probability help will be needed is (Round to four…
The state of California has a mean annual rainfall of 19 inches, whereas the state of New York has a mean annual rainfall of 48 inches (Current Results website, October 27, 2012). Assume that the standard deviation for both states is 4 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken. a. Show the probability distribution of the sample mean annual rainfall for California. This is a normal probability distribution with and (to decimals). b. What is the probability that the sample mean is within inch of the population mean for California? (to decimals) c. What is the probability that the sample mean is within inch of the population mean for New York? (to decimals) d. In which case, part (b) or part (c), is the probability of obtaining a sample mean within inch of the population mean greater? Why? The probability of being within inch is greater because the sample size is .

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