Why is it that the normal distribution is the most useful probability distribution?

Q: There are 4 treatments, so we have k4 and k-1- A total of 18 men undenvent Treatment 1 giving n, -…

A: The number of treatments k is 4.

Q: Explain Student t distribution & F distribution?

A: Student t distribution: Shape of a student’s t distribution is bell shaped curve with mean zero and…

Q: Illustrate probability density function of a normally distributed random variable?

A: f(x)=12πσ2e-(x-μ)22σ2   -∞<x<∞     X~N(μ,σ2)

Q: A surfboard factory just discovered a manufacturing error that causes some of the surfboards to…

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Q: Anticipated consumer demand in a restaurant for free -range steaks next month can be modeled by a…

A: Let X be the Anticipated consumer demand in a restaurant for free -range steaks next month can be…

Q: If a distribution is normal, then it is not possible to randomly select a value that is more than 4…

A: Given : We have given normal distribution .

Q: The probability of any one particular value in the normal distribution

A: The probability value always lies between 0 and 1 for any distribution.

Q: Students mark on an exam has a normal distribution with a mean of 65 and SD 10. What is the…

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Q: Using Chebyshev's theorem and the normal distribution, compare the probability that a number will…

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Q: Computers are commonly used to randomly generate digits of telephone numbers to be called when…

A: The probability  of getting a digit less than 3 = 310…

Q: A drug tester claims that a drug cures a rare skin disease 76​% of the time. The claim is checked by…

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Q: What probability distribution might you use to describe the number of COVID19 infections per…

A: The Poisson and Binomial distributions are the discrete probability distributions. Whereas, the…

Q: The temperature of heated water is in a coffeemaker is a continuous random variable that follows a…

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Q: Percentage daily returns on a financial asset is modelled through a normal random variable. You want…

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Q: The t-distribution is a probability distribution that is used to estimate population parameters when…

A: If we have to estimate the population parameters and the sample size is greater than 30 , we use…

Q: What are the conditions for using a normal distribution to approximate a binomial distribution?

A: In probability distribution, the binomial distribution is a discrete probability distribution with…

Q: If all normal distributions have the same shape, how do they differ?

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Q: The mean value of the Poisson probability distribution is numerically equal to its standard…

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Q: When figuring probabilities for a normal distribution why is it necessary that we must convert to a…

A: For figuring out the probabilities for a normal distribution,whatever the parameters might be,we…

Q: A drug tester claims that a drug cures a rare skin disease 65 ​% of the time. The claim is checked…

A: The mean is, μ=np=100×0.65=65 The standard deviation is, σ=np1-p=100×0.65×1-0.65=22.75=4.7697 The…

Q: A drug tester claims that a drug cures a rare skin disease 75% of the time. The claim is checked by…

A: Given, ( n = 100 ): Number of patients tested.( p = 0.75 ): Probability of a patient being cured as…

Q: erature of healthy humans has a normal distribution with mean 98.3°F and variance 0.5375. What is…

A: The standard deviation is calculated as: σ=0.5375=0.73314≃0.733 Given:μ=98.3, σ=0.733 The…

Q: What are the three requirements of linear regression?

A: these are the following three requirement of linear regression

Q: How can we calculate the probability-weighted average of the squared deviations?

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Q: Computers are commonly used to randomly generate digits of telephone numbers to be called when…

A: No, we cannot use the methods of this section, because the distribution of randomly generated…

Q: Is the probability for my standardized range really the same as for my original distribution? How…

A: introduction the above question is about probability  We have to explain is the probability for…

Q: A drug tester claims that a drug cures a rare skin disease 72​% of the time. The claim is checked by…

A: Given,n=100p=0.72mean(μ)=np=100×0.72=72standard deviation(σ)=npqσ=100×0.72×(1-0.72)=4.48999

Q: The combined probability distribution of two random variables is referred to as its marginal…

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Q: It is possible to obtain a probability of .000001 under the normal curve? True or False Can you…

A: Solution: The given statement is “It is possible to obtain a probability of 0.000001 under the…

Q: Statistical Literacy, Consider two discrete probability distributions with the same sample space and…

A: The probability distributions with same sample space are given below: The mean is, Thus, the mean…

Q: Distinguish between the Binomial and Poisson probability distributions.

A: Answer:- Binomial distribution describes the distribution of binary data from a finite sample. Thus…

Q: What is the difference between uniform distribution and binomial distribution?

A: The two distributions which are given are Uniform distribution and Binomial distribution.

Q: The standard normal curve is a normal probability distribution that has a mean of 1 and standard…

A: standard normal distribution:-x~N(μ,σ2) then z=x-μσ~N(μ=0,σ2=1)               ~N(0,1)is called…