Explain the following with Business related or daily life examples: Binomial Distribution and Poisson Distribution. Support your answers by solving one part manually way and the other parts by using Excel.

Q: Question 4 Let X be a normal random variable with mean μ = 3 and standard deviation σ = 2. Compute…

A: Mean(μ) = 3standard deviation(σ) = 2

Q: The probability distribution of X is given as: f(x) = { 0.4; x = 1 (x-1)/4; 1 < x < 2 (3-x)/4; 2…

A:

Q: During business hours, the number of calls passing through a particular cellular relay system…

A: The average no.of calls passing through a particular cellular system ()= 5 per minute A random…

Q: Brandy is sorting through her many pairs of socks, and is counting how many of each color she has.…

A: The number of white pairs of socks is 48. The number of black pairs of socks is 52. The number of…

Q: random variable X is given in the following table. Find the standard deviation of the random…

A: PMF of Xx-2-1012P(X =x)0.160.170.300.150.22

Q: Need help - In how many ways can a class of 15 students be divided into 5 groups of 3 students in…

A: Given:A class of 15 students needs to be divided into 5 groups of 3 students each, with the…

Q: Suppose that a random variable X has the following probability density function. f(x) = { 0 SC…

A: f(x)=c(64-x2); 0≤x≤8

Q: A TV executive is interested in the popularity of a particular streaming TV show. She has been told…

A: It is required to find the probability that all 6 of the households in the city being monitored by…

Q: Consider the unit cirlce in the plane; that is, the set of all points within a distance of 1 of the…

A:

Q: The number of tickets issued by a meter reader for parking- meter violations can be modeled by a…

A: It is given that, the number of tickets issued by a meter reader for parking meter violations…

Q: Flip a balanced die 5 times. Let X be the total number of 5 or 6. Then, X ~?, E(X) =?, V(X) =?.

A: Flip a balanced die 5 times &amp; Let X be the total number of 5 or 6.Number of trials =5Find X…

Q: Use the geometric distribution to derive E(Y), E(Y^2), and V(Y) from the Poisson distribution

A: The geometric distribution and Poisson distribution are two different types of probability…

Q: x y 59.9 72.8 61.4 128.8 33.2 7.2 41.4 -111.7 61.9 160.4 50.3 130.4 47.4 -65.7 43.2 -37.7 48.2 190.5…

A: From the provided information,…

Q: You wish to hire Ricky to manage your new Chicago office. The profits will depend partially on how…

A: Given the probability table:Profit = $100,000Profit = $20,000Lazy / Gaming20%80%Engaged / Hard…

Q: If P(A) = 0.5, P(B) = 0.7 and P(AUB) = 0.6, what is P(An B)?

A: P(A)=0.5P(B)=0.7P(AB)=0.6

Q: Mike's game consists of selecting two balls, without replacement, from an urn containing 7 balls…

A: To calculate how much Mike should charge to play this game if he wants to make $0.90, on average,…

Q: 1. Your garage door has a keypad with the numbers 0-9. You need to pick a 5-digit lock code. How…

A: (As per our standard guideline we are supposed to answer only 1 question.)1) Given:The garage door…

Q: X~N(0,1) and find the probability density function of the random variable Y=IXI.

A: Probability Distributions: You should be familiar with probability distributions, including the…

Q: Calculate the probability that the gold component is neither sufficiently pure nor sufficiently…

A: The quality of a manufactured gold component is assessed for both its purity and its…

Q: Card Mom their own deck. Compute the probabi a. Bert and Ernie both draw an Ace. 1/169 b. Bert draws…

A: We know thatThere are 52 cards in the deck divided into two colour i.e red (26) and black (26).…

Q: 5. Suppose that E[X] = 2 and Var(X) = 6. (a) Compute E[(X + 1)²]. (b) Compute Var(4 + 3X). (c)…

A: E(X)=2, V(X)=6

Q: Describe a conditional probability activity. What makes it conditional/ independent? Use associated…

A: Activity: Drawing a Face Card Given That We've Drawn a Red CardSuppose we draw a card at random from…

Q: Compute the number of passwords possible that satisfy these conditions: Password must be of length…

A: Password Length: You need to know the length of the password, which is given as 5 characters in this…

Q: A city planner surveyed 144 residents. For each, the planner recorded whether the resident owns a…

A: a)The table defines the number of residents, who own a card and whether the residents live alone.

Q: In this problem, we will approximate a binomial dis- tribution by a normal distribution. From…

A: X~Bin(n,p)

Q: Oil pipes ~ Oil field pipes are internally coated in order to prevent corrosion. Researchers…

A: Standard deviations=σ=0.5,α=0.05,marginoferror=e=0.15

Q: Students were surveyed on campus about their study habits. Some said they study in the morning,…

A: Total number of students=42

Q: On average, 2 traffic accidents per month occur at a certain intersection. Complete parts (a)…

A: On average, 2 traffic accidents per month occur at a certain intersection.X~Poisson(λ=2)Note:…

Q: the following table organizes a sample of tri-state residents by their sports fandom: new york -…

A: The following table organizes a sample of tri-state residents by their sports fandom:ResidentYankee…

Q: For a standard normal distribution, find the probability a score is at most 0.37 standard deviations…

A: Here given , score follows standard normal distribution with mean 0 and standard deviation 1.X =…

Q: What is the probability that a randomly chosen flashlight lasts more than 100 hours? R. 0.41 b)…

A: One boat contains 3 different types of disposable flashlights.The probability that a type 1…

Q: Suppose that the waiting time X (in seconds) for the pedestrian signal at a particular street…

A: The random variable   represents the waiting time for the pedestrian signal. The PDF of random…

Q: (a) (c) = 0.9854 (b) P(0 ≤Z≤ c) = 0.2995 (c) P(c≤ Z) = 0.1271

A:

Q: The distribution of hourly wages of employees of the TNON company obeys a normal law whose average…

A: Mean Standard deviation

Q: Assume a member is selected at random from the population represented by the graph. Find the…

A: X~N( μ , ?)μ=20.2    , ?=5.4Z-score =( x - μ )/?

Q: On a popular app, users rate restaurants as  1 ,  2 ,  3 ,  4 , or  5  stars. Suppose a rating…

A: Value of x12345P(X=x)0.230.180.110.260.22

Q: 1.Firstly, I think in the first part of the question, you make a mistake on calculation, see image…

A: Try in this way using the concept of Order Statistics.This will simplify your problem.

Q: Machinists who work at a tool-and-die plant must check out tools from a tool center. An average of…

A: arrival rate =lambda= = 10 machinist per hourThe service rate () = 5 min to hander per request…

Q: Suppose that we have a deck of 30 cards. Both sides of the first 10 cards are colored red, both…

A: Given: Let R be the event that the top side of the top card is red.Let B be the event that the…

Q: Each time a player plays a certain card game, there is a probability of 0.15 that the game will work…

A: It is given that each time a player plays a certain card game, there is a probability of 0.15 that…

Q: (d) (e) Using the marginal density of Y from (b), find the probability that the walk-up window is in…

A: Let X and Y have joint pdf

Q: well-balanced die is rolled 300 times. Find the probability that the [1] appears between 55 and 60…

A: n=300, P(55≤X≤60)=?

Q: The state lottery board is examining the machine that randomly picks the lottery numbers. On each…

A: Number of trials for experimental probability is 20.Number of trials for theorotical probability is…

Q: Consider the unit cirlce in the plane; that is, the set of all points within a distance of 1 of the…

A: To find the probability density function (pdf) for the distance B=X2+Y2 from the origin to a point…

Q: Suppose X is a random variable taking possible values in {1, 2, 3,... } and 0 < P(X = 1) < 1, and…

A: Let X be the random variable having possible values {1,2,3...} and 0&lt;p&lt;1X satisfies the…

Q: Given the data set below, calculate the range, mean, sample variance, and sample standard deviation.…

A: Given thatData values :  25 , 35 , 19 , 38 , 16 , 16 , 8 , 29 , 47Sum of data values = 233Number of…

Q: The scores on the Accuplacer test and High School GPAs are normally distributed. The Accuplacer test…

A: The mean of the Accuplacer test, The standard deviation of the Accuplacer test, The mean of the High…

Q: Judah is very fond of candies; he always has a few in his pockets. To add variety to his candy…

A: Given that Judah is very fond of candies; he always has a few in his pockets. He plays a game to…

Q: Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die…

A: Given events are,A: the red die shows 2;B: the numbers add to 5;C: at least one of the numbers is…

Q: . Suppose X ~N(3.7, 1.28). Let Y = -0.5X + 14. Then, P(X <= 5.0) =?, E(Y ) =?, and V(Y

A: