A certain factory produces X, specialized parts on day n, where X, are independent and identically distributed random variables with mean 6 and variance 9. Let S, be the total number of specialized parts produced from day 1 to day n. Using central limit theorem, determine the total number of parts, a, the said factory can guarantee to produce by day 50 with at least 99.9% certainty, i.e. determine the maximum value of a so that P(S50 2 a)> 0.999. Note: This maximum value must be a whole number.

Q: large construction firm follow a Poisson distribution with a parameter of 4. Compute the probability…

A:

Q: Steel produced by company A has an average tensile strength of 4500 lbs and a variance of 40000 lbs,…

A: Solution: Given information: nA= 50  Sample size of company A nB= 100 Sample size of company  B μA=…

Q: The usage time of a telephone belonging to a specific brand may be looked upon as a random variable…

A:

Q: The number of cakes baked on any business day in this bakery is a random variable that follows a…

A: The number of cakes baked on any business day in this bakery is a random variable that follows a…

Q: The burning life( in hours )  of  electric lamps installed in a street of a city follows a normal…

A:

Q: If X1, X2 and X3 are three independent, normal random variables with expected values 10, 20, and 15…

A: From the given information, expected values 10,20 and 15 and variances 5, 3, 4 respectively. That…

Q: The strength of the cubic concrete of the first line production is 110 N/mm² and standard deviation…

A: Let 'X' represent the strength of the cubic concrete of the first line production, and 'Y' represent…

Q: Suppose the network flow size is a normal random variable with parameter μ = 71 GBytes and σ = 2.5…

A: It is given that, Population parameter, Standard deviation, The network flow size   is a normal…

Q: A large genetic pool contains 65 percent of allele ‘A’ and 35 percent of allele ‘a’. If 20 alleles…

A: Given that P(allele A)=65%=0.65 and P(allele a)=35%=0.35 The expected number of allele 'A' among 10…

Q: 4. Researchers working for a sports drink company would like to know if a new blend if its popular…

A: The Alternative hypothesis is define as that you might believe to be true or hope to prove true

Q: nue to hold exhaustively for the population of that village. Let X om variable representing the…

A:

Q: M(rapid eye movement) sleep is sleep during which most dreams occur. Each night a person has both…

A:

Q: A box contains 5 Balls labeled with the number "1", 3 balls labeled with the number "2", and 1 ball…

A:

Q: The 10-yr and 25-yr floods of a certain river are respectively, 73 m3/s and 84 m3/s. Based on the…

A:

Q: A random variable Y has the Gaussian distribution on R with mean u and variance o?, Select all the…

A: P(Y≥y)≤12πσ2exp-y-μ2/2σ2 for all yℂℝ because it is also a part of normal distribution.

Q: a ) Calculate the expected value, the variance and the standard deviation of 2X1 - 0.5X2 + X3 .…

A: Normal distribution is also known as the Gaussian distribution . It is a bell-shaped , symmetric…

Q: Mean lifetime of these batteries (i) (ii) Probability that such battery will last more than 300 hrs.

A:

Q: The number of customers arriving at a teller’s window at Commercial Bank is Poisson distributed with…

A: It is given that the number of customers arriving at a taller's window at the commercial Bank is…

Q: Provide an example of a random variable with variance of 0

A: Given that We have provide example of random variable with variance of 0

Q: Anna´s expenses for entertainment during a period of time can be described with a normally…

A: Introduction: Denote X1 as the entertainment expense for Person A in a single period of time, and X2…

Q: Let X be a random variable representing the number of times that you have to roll two dice until you…

A: Here, the given context follows negative binomial distribution with k = 10 and p = 118 (probability…

Q: The range of random variables X is [0,a,b,c,x] where x is unknown. If each value is equally likely…

A: The random variable X takes the values 0, a, b, c. & x where a= 1, b = 2, c = 3. Since there are…

Q: Two machines at a factory are supposed to produce 50 mm nails. The lengths of nails from Machine A…

A: It is given that the length of the produced nails follows normal distribution with mean 50 mm and…

Q: Let x be a random variable that represents red blood cell (RBC) count in millions of cells per cubic…

A: Hypothesis testing is conducted for the parameters of the population like population mean,…

Q: Let X₁, X2, X, be normal random variables with mean and variance 2. What are the method of moments…

A: X~N(μ,σ2)

Q: The mean number of typhoon hitting US follows a Poisson distribution with     variance 0.5 per…

A: In general, the mean and variance of the Poisson distribution is same. Here, ?=0.5 per month. a)…

Q: Let wages denote a person's hourly wages and edu denote their years of education. Suppose that…

A: The relationship between "wages" and "education" is .Where,The error term follows .The given value…

Q: Use the result of Exercise 45 to show that, if n independent random variables Xi have normal…

A: The mean is calculated as follows:

Q: Let X denote the random variable that gives the sum of the faces that fall uppermost when two fair…

A: In general, there are 36 possible outcomes when rolled a pair of balanced dice.

Q: Let a random experiment be the casting of a pair of fair five-sided dice and let X equal the maximum…

A: Given, 2 fair dice are thrown simultaneously. Each die has 5 sides. X: The maximum of two outcomes.…

Q: wo suppliers manufacture a plastic gear used in a laser printer. The impact strength of these gears…

A: Given, A random sample of 10 gears from supplier 1 results in x1 = 290 and s1 = 12, and another…

Q: 1. A manufacturer of marble countertops for kitchen countertops manufactures them in Venetian marble…

A: A manufacturer of marble countertops for kitchen countertops manufactures them in Venetian marble…

Q: The number of employed persons in Mexico between 2009 and 2019 can be modeled as a random variable…

A: Solution: Let X be the number of employed persons in Mexico between 2009 and 2019. From the given…

Q: The total compilation time of a computer program has Gamma distribution with average u=10 minutes…

A: Mean=μ=10, Variance=σ2=50  Let X be the program

Q: the environmental protection agency (EPA) limits the amount of vinyl chloride in the plant air…

A: Given Information :  The environmental protection agency (EPA) limits the amount of vinyl chloride…

Q: 2. A certain factory produces X, specialized parts on day n, where Xn are independent and…

A: Central Limit Theorem: When sampling represents the normal distribution and the size of the sample…

Q: drug for a year and has 0 colds in that time, how likely is it that the drug is beneficial for him…

A:

Q: Rods are produced in large quantities in a factory. The masses of these rods are normally…

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

Q: is rolled repeatedly until a 6 falls uppermost. Let the random variable X denote the number of times…

A: A game of rolling a die will stop only when the a player will get 6 .  The game can stop in 1 throw…

Q: An analysis of personal loans at a local bank revealed the following facts: 10% of all personal…

A: P(D)=10% , P(D')=90%, P(H|D)=20%, P(H|D')=70% P(H∩D′)=?

Q: The number of fish that a person catches per hourat Woods Canyon Lake is a random variable having…

A: Let the random variable X, be the person catches number of fish per hour. Let X follows a Poisson…