7 In the production process of cups, it is known that on average 40 cups have cracks in every 1000 cups produced. (a) Find the probability that at most three cups having cracks in a random sample of 10. (b) If the probability that no cups in k cups selected at random, having cracks is 0.12, determine the value of k. (c) Find the probability that more than two cups have cracks in a random sample of size 200.

Q: In a prohibited area 12 security guards are assigned (posted) at a certain distance. A random check…

A: Consider X be a random variable which follows binomial distribution indicates the number of security…

Q: In a chemical plant, 20 holding tanks are used for final product storage. Five tanks are selected at…

A: There are total 20 holding tanks. Out of them 6 contains high viscosity material. Hence, 20-6 = 14…

Q: In analyzing hits by certain bombs in a​ war, an area was partitioned into 552 ​regions, each with…

A: In this case μ represents 'mean number of hits per region'. The value of m is calculated as follows:…

Q: Q1. Sixteen red balls have numbers from 1 to 16. If a ball is drawn at random, find: 1- probability…

A:

Q: A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 17…

A: Binomial distribution: The binomial distribution gives the probability of number of successes out of…

Q: A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 16…

A: Assume,  X be the random variable representing the number of defective pens in sample. p be the…

Q: he manager of Toy World has decided to accept a shipment of electronic games if none of a random…

A: This problem can be solved using the binomial distribution formula.

Q: 10% of HCT students have overweight. 20% of HCT students get grades greater than or equal to A-. One…

A: Given that: 10% of HCT students have overweight. This means P(overweight)= 10%=0.10

Q: A certain manufacturing process yields electrical fuses of which, in the long run 15% are defective.…

A:

Q: A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 16…

A:

Q: 10. Let the discrete random variable X be the number of odd numbers that appear in 16 tosses of a…

A: Let X be the number of odd numbers that appear in 16 tosses of a fair die  Probability that an odd…

Q: A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 16…

A:

Q: A factory tests a random sample of 27 transistors for defects. The probability that a particular…

A: P(defective) = 0.03 Therefore, P( non defective ) = 1 - 0.03 = 0.97

Q: A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 19…

A:

Q: 04: A group of 30 manufactured of concrete pipes contain 8 defective pipes and 22 non-defective…

A: Given: A group of 30 manufactured pipes contains 8 defective and 22 non-defective pipes. A sample of…

Q: A machine that manufactures automobile parts produces defective parts 12% of the time. If 10 parts…

A: X~Binomial(n,p)

Q: A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 19…

A:

Q: A machine that manufactures automobile parts produces defective parts 11%of the time. If 8 parts…

A:

Q: 10. In a long production run, 1% of the components are normally found to be defective. In a random…

A: Binomial Distribution: If we have n trials each having two outcomes, say Success and Failure, trials…

Q: A machine that manufactures automobile parts produces defective parts 16 % of the time. If parts 8…

A: Consider success as the event that the automobile part is defective. Hence, p=P(Success)= 0.16. Let…

Q: high-speed robotic conveyor in an egg-processing facility handles eggs one by one, but breaks, on…

A: From the given information we want to find the given probability. Breaks 3.3 eggs out of 1000

Q: Researchers are interested in the popularity of the new HPV vaccine among a population of university…

A: The given information is: Number of trails (n)=7 The probability that at least one of the three…

Q: Suppose that a radio contains six transistors, two of which are defective. Three transistors are…

A: 7. Given that the radio contains 6 transistors, two of which are defective. Three transistors are…

Q: The unemployment rate in a city is 16%. If 7 people from the city are sampled at random, find the…

A: Given that the unemployment rate in a city is 16%. Probability, p = 16% Sample size, n = 7

Q: A vegetable basket contains 12 peppers, of which 3 are red,  are green and 5 are yellow. Three…

A: Given No. of red peppers = 3 No. of green peppers = 4 No. of yellow peppers = 5

Q: The unemployment rate in a city is 13%. If 6 people from the city are sampled at random, find the…

A:

Q: 5 Estimates for the proportion of people who have COVID-19 in a given community vary over time and…

A: Givenp=0.04n=20Let "x" be the no.of people is infected…

Q: Determine the probability that 3 out of 5 articles drawn at random from 100 articles are defective,…

A: Given that the articles are drawn one at a time with replacement and mixing. So the probability of…

Q: Each sample of water has a 10% chance of containing a particular organic pollutant. Assume that the…

A: Let X be the random variable from binomial distribution with probability (p) = 10% = 0.10 and sample…

Q: A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 19…

A: (a) Consider that shipment is accepted if no more than two defective pens

Q: A manufacturing process has a 70% yield (meaning that 70% of the products are acceptable and the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A computer laboratory in a school has 33 computers. Each of the 33 com- puters has 90% reliability.…

A: GivenNumber of computers in school = n = 33Probability of computer working = p = 0.9 1) Let X be…

Q: How is it that K= 0 in this specific question   A univeristy found that 20% of its students withdraw…

A: Let X denotes the number of statistic students who withdraw the course and it follows binomial…

Q: factory tests a random sample of 19 transistors for defects. The probability that a particular…

A: Here we want to know the probability that there is no defective transistor in the Sample.

Q: Using a computer program that can generate randomintegers on the interval (0, 9) with equal…

A: Using R programming software to compute the probabilities.

Q: The unemployment rate in a city is 15% . If 8 people from the city are sampled at random , find the…

A: The sample size n is 8 and p value is 0.15.

Q: A factory received a shipment of 14 flanges, and the vendor who sold the items knows there are 8…

A: Solution: a. From the given information, there are 14 flanges. Out of which there are 8 flanges are…

Q: A random sample of 8 articles is taken from a large  batch of manufactured articles and the batch is…

A: It is an important part of statistics. It is widely used.

Q: Exercise 1. In a manufacturing process where glass products are made, defects or bubbles occur,…

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

Q: A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 16…

A: Let the R.V X denotes the number of defective pens and it follows the binomial distribution with…

Q: A stationary store has decided to accept a large shipment of ball-point pens if an inspection of 15…

A:

Q: 4. The battery life of a fully charge iPhone 13 Pro on a standby follows a normally distributed with…

A: Using R code

Q: A box in a certain supply room contains three 40-W lightbulbs, five 60-W bulbs, and seven 75-W…

A: Given data: 3 = 40-W lightbulbs, 5 =  60-W bulbs, and  7 =  75-W bulbs. Suppose that three bulbs are…

Q: A random number generator produces sequences of independent digits, each of which is as likely to be…

A: Solution:  Let X denotes any single digit.  The possible values of X are 0,1,2,3,4,5,6,9. Each…

Q: 5. From company records, a manager knows that the probability that a defective article produced by a…

A: (a) Let X be the number of defective articles from binomial distribution with probability (p) =…

Q: A certain reagent is created to test for an infectious disease. The test has an accuracy rate of p =…

A: Answer:  a) Let X be the number of patient receive accurate test results. X ~ Binomial(n = 4, p =…

Q: 2. Give the probability generating function for an offspring distribution in which an individual…

A: Probability generating function of an offspring distribution =? An individual either dies with…

Q: Samples of 20 parts from a metal punching process are selected every hour. Typically, 1% of the…

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.