A foreman for an injection-molding firm admits that on 52% of his shifts, he forgets to shut off the injection machine on his line. This causes the machineto overheat, increasing the probability that a defective molding will be produced during the early morning run from 4% to 22%. The plant managerrandomly selects a molding from the early morning run and discovers it is defective. What is the probability that the foreman forgot to shut off themachine the previous night?Probability =

Let us define some events A : the forman forget to shut off the machine. B : the forman does not…

Answered: A foreman for an injection-molding firm…

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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After examining her college attendance records for the past few years, Professor Bea Earlee determined that there is a 30% chance that a student will come late to her class. Six students are selected at random. Find the probability that none of the six arrive late to class. Round to 4 decimal places.
It is known that roughly 2/3 of all human beings have a dominant right foot or eye. Is there also right-sided dominance in kissing behavior? An article reported that in a random sample of 121 kissing couples, both people in 75 of the couples tended to lean more to the right than to the left. (Use a = 0.05.) USE SALT (a) If 2/3 of all kissing couples exhibit this right-leaning behavior, what is the probability that the number in a sample of 121 who do so differs from the expected value by at least as much as what was actually observed? (Round your answer to four decimal places.) (b) Does the result of the experiment suggest that the 2/3 figure is implausible for kissing behavior? State the appropriate null and alternative hypotheses. O Ho: P = 2/3 H₂: P = 2/3 O Ho: P = 2/3 H₂: P > 2/3 O Ho: P = 2/3 H₂: p ≤ 2/3 O Ho: P = 2/3 H₂: P < 2/3 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) Z…
Suppose a life insurance company sells a $250,000 1-year term life insurance policy to a 20-year-old female for $300. According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is 0.999544. Compute and interpret the expected value of this policy to the insurance company.
Suppose a life insurance company sells a $260,000 1-year term life insurance policy to a 20-year-old female for $170.According to the National Vital Statistics Report, 58(21), the probability that the female survives the year is 0.999544.Compute and interpret the expected value of this policy to the insurance company.
An investigative bureau uses a laboratory method to match the lead in a bullet found at a crime scene with unexpended lead cartridges found in the possession of a suspect. The value of this evidence depends on the chance of a false positive-that is, the probability that the bureau finds a match, given that the lead at the crime scene and the lead in the possession of the suspect are actually from two different "melts," or sources. To estimate the false positive rate, the bureau collected 1,809 bullets that the agency was confident all came from different melts. Then, using its established criteria, the bureau examined every possible pair of bullets and found 606 matches. Use this information to compute the chance of a false positive. Is this probability small enough for you to have confidence in the agency's forensic evidence? Choose the correct answer below and fill in the answer box to complete your choice. (Round to four decimal places as needed.) O A. The chance of a false positive…
Suppose that we have test for lung cancer, which correctly identifies those with the cancer 70 % of the time, and mistakenly identifies those without the cancer 5 % of the time. In the cohort of interest, the rate of this cancer is somewhat low: 0.9 %. Find the probability -- a number between 0 and 1 -- that someone diagnosed (testing positive) with this test actually has lung cancer.
A blockchain-based business received consensus validation via two different systems A and B. The time between validations for each validation system in a typical day is known to be exponentially distributed with a mean of 3.2 seconds. Both systems operate independently. Given the above distribution, the probability that no validation will be received from system A in a 5-second period is (expressed your answer in 4 decimal places). Likewise, the probability that no validation will be received from both systems in a 5-second period is (expressed your answer in 4 decimal places). If X denotes the number of validations in a 5-second interval. Then, X is a Poisson random variable with the lambda is equal to (expressed your answer in 4 decimal places). Then, the probability that both systems receive two validations between 10 and 15 seconds after the site is (expressed in 4 decimal places). officially open for business is
3. Suppose X and Y have joint probability density function f(x, y) = {* S6x, 0 < x< 1,0 < y <1- x elsewhere. Determine whether the two random variables are dependent or independent. b. If the value of Y is 0.5, what is the probability that X will have a value greater than 0.3? а.
Question 9 A batch of 400 LEDS contains 7 that are defective. This is known to be the long-term average for the production. The company sells boxes with 50 LEDS in each box. (a) What is the probability there are 1 or more defective bulbs in a box? (b) If three LEDS are selected at random from a box, what is the probability that the third one selected is defective given that the first one selected was not defective and the second one selected was defective? (c) Boxes are returned if 3 or more are defective. What is the probably a box will be returned?
An antique collecter has been following the price of a certain old camera and he found out that the camera's price changes each day and it can either rise or fall in value. The price changes per day are assumed to be independent events. After observing the price for 8 months, he found out that the price rose for 40% of the days and it sunk for the rest. He wants to determine the probability that the camera will be a certain value on a particular day so he asked you for help. 1) What distribution does this problem follow? (Geometric, Binomial, Poission?) 2) Determine the probability that 7 days from now, the cost of the camera will be the same as it is today.3) Determine the probability that the camera's cost has increased from its current value after 5 days.
Question 6 Company records show that the proportion of defective parts has historically been 5%, however a quality control engineer believes that due to budget cuts these numbers have increased. To test this claim a random sample of N = 15 parts will be taken and if more than two defective parts are found the inspector will conclude that the proportion of defective parts has increases. Calculate the probability of the type one error. 18.5% 81.5% О 3.6% O 96.4%
It is estimated that one in twenty-five Americans is a cystic fibrosis carrier. Find the probability that a randomly selected American couple's child will have cystic fibrosis (assuming that they are unrelated). (Enter your answer to four decimal places.)

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