Suppose X is a binomial random variable with n=100 and p=0.3. Estimate P(X=40) by using the normal approximation.

Q: Suppose that f(x) = e for 0 <x Determine the mean and variance of the random variable.

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Q: The

A: It is given that the sample size is n=50. The probability that a workforce belongs to a union is…

Q: Suppose that the number of customers who enter a bank in an hour is a Poisson random variable, and…

A: Given problem Given that   Suppose that the number of customers who enter a bank in an hour is a…

Q: Suppose Y₁, Y2,, Yn is an iid sample from a Poisson(A) distribution, where > 0. Is Y a consistent…

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Q: Suppose that X is a binomial random variable with n = 100 and p=0.5. Find the probability P is less…

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Q: If the probability of a defective bolt is 1/10, find (i) the mean; (ii) variance; (iii) moment…

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Q: Suppose that X is a binomial random variable with = 200 and p = 0.4 a. find the probability P(X ≤…

A: X~Bin(n, p) n = 200 p = 0.4 Mean(X¯) =n×p Mean(X¯) =200×0.4 Mean(X¯) =80 σ = n×p×(1-p) σ =…

Q: Suppose that f (x) = e-* for 0 < x Determine the mean and variance of the random variable.

A: Given problem Given that   Suppose that  f(x) = e-x for 0 &lt; x  The mean and variance of the…

Q: Suppose the force acting on a column that helps support a building is a normally distributed random…

A: GivenMean(μ)=13.0standard deviation(σ)=1.5

Q: Let X be a binomial random variable that is binomially distributed with a mean of 9 and a variance…

A: binomially distributed with a mean of 9 and a variance of 6. Find q =?

Q: Suppose we have a random variable X distributed as a Bernoulli distribution with p = 0.5. What is…

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Q: Suppose that a random variable X is normally distributed with a mean of 200 and a variance of 625.…

A: The random variable X is normally distributed. The population mean is 200. The population variance…

Q: for a normally distributed random variable X with mean of 177.15 and standard deviation of 4.95 a…

A: It is given that the mean is 177.15 and the standard deviation is 4.95.

Q: Suppose that the random variable has the binomial distribution, X - B(100, 0.2) , and is the…

A: Here it is given that X~Bin(100,0.2) where n=100 and p=0.2.

Q: Suppose that X and Y are random variables where the conditional expected value of Y given X is given…

A: # random variable x and y such given  E(y/x)=3*X+6  E(x)=0 &amp; var(x)=9  Then to find minimum…

Q: The normal random variable with mean = 0 and standard deviation = 1 is said to have the…

A: If X is random variable from standard distribution with mean(mu) = 0 and standard deviation (sigma)…

Q: The test of equality of the variances between two normally distributed populations relies which has…

A: We have to find the distribution of random variable which is used in testing the equality of…

Q: Suppose that the random variable X has mean u and variance o >0. What are the values of a and b>0…

A: Given data: The given expression is Y=a+bX. The given mean is μ=0. The given variance is…

Q: Assume the probability that a maple tree at age 5 grows less than 130 cm is equal to 0.1. If the…

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Q: The random variable X has a normal distribution with a variance of 16 and an unknown mean. If the…

A: Given Data: X is a random variable   Variance (X)=16   X~ Normal (μ, 16) P(x&gt;65)=0.025

Q: Suppose that on average 2 people in a major city die each year from alien attack. Suppose that each…

A: Poisson approximation is given by:

Q: Suppose that it is known that in a certain community 30% of the households have a micro-wave ovens.…

A: Given: Population proportion p = 30% p =  0.30 Sample size n = 19 Formula Used: Standard deviation =…

Q: Consider a binomial experiment with n = 20 and p = 0.4. Calculate the P(X ≥ 10). Do not use normal…

A: Given that  n=20 , p=0.4 X~Binomial(n=20 , p=0.4)

Q: Suppose X is a normal random variable with mean 20 and standard deviation of 4. What is th…

A: Let X be the random variable from normal distribution with mean (μ) = 20 and standard deviation (σ)…

Q: Suppose X is a binomial random variable with n=100 and p=0.3. Estimate P(X=40) by using the normal…

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Q: Suppose that x is a normally distributed random variable with mean 5 and standard distribution is 6.…

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Q: If x, x2 ... Xn is a random sample from N (µ, o²) popula- tion, find sfficient estimator for µ and…

A: ANSWER: For the given data,

Q: Suppose X is a random variable with a mean of 10 and a variance of 100. suppose Y is a random…

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Q: A random variable has a normal distribution withσ = 10. If the probability that the random variable…

A: A z-score describes the position of a raw score in terms of its distance from the mean, when…

Q: A simple random sample of size n=14 is obtained from a population with μ=67 and σ=19.   Assuming…

A: From the given information, Consider,  Sample size (n) = 14 Population with μ=67 and σ=19. Thus,

Q: Suppose the random variable X has a geometric distribution with p=0.7. Find P(X>1) ?

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Q: Let X be a random variable with a variance of 2. Find the variance of 5X+5. Answer: Var(5X+ 5)=

A: We can find the answer as below

Q: The figure on the right displays the randomization distribution for testing 0OL = rd"H versus H p >…

A: The sample mean of 12 is in very right most side from the mean (100). Therefore, the p-value would…

Q: If X is distributed as normal with μ = 20 and σ2 = 40 and a random sample of 4 variates is drawn…

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Q: Suppose that the mean weight of a particular type of ripe tomato is 155 g, and the variance of the…

A: Assume a random variable X, which is the weight of a particular type of ripe tomato.

Q: . Suppose that X is a binomial random variable with n = 200 and p = 0.4. Find the probability PCX<…

A: As per our guidelines we are supposed to answer only one question per post hence I am solving first…

Q: Suppose X is a random variable with standard beta distribution and parameters (alpha) = 8 and (beta)…

A: Suppose X is a random variable with standard beta distribution and parameters (alpha) = 8 and (beta)…

Q: Suppose that X is a normal random variable with mean 5. If P(X > 9) = 0.2 ,approximately what is…

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Q: Suppose x is a normally distributed random variable with mean u =0 and standard deviation o = 1.…

A: We'll use formula here and using table we will find the value here . and after that convert that…

Q: Suppose the lifespan (in months) of a smartphone battery can be modeled as a continuous random…

A: Given,F(X)=1-e-x3   ;  x≥0

Q: For a normal population with µ = 60 and σ = 50, the distribution of sample means based on n = 25…

A: Given that, Mean = 60 Standard deviation = 50 Sample size = 25

Q: Suppose two independent random samples of size n1 = n2 = 10 are from a normal population. Assume the…

A: From the given information, n1=n2=10 numerator degrees of freedom=10-1=9 Denominator degrees of…

Q: Suppose Y is a continuous random variable with uniform distribution having mean 1 and 4 What is P(Y…

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Q: If X is a normally distributed random variable with mean equal to 1 and standard deviation σ and if…

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!