A normal distribution has a mean of 31 and a standard deviation of 6. Find the probability that a randomly selected x-value from the distribution is in the given interval

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Q: The length of time it takes to find a parking space at 8am follows a normal distribution with a mean…

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A: The normal distribution: A continuous random variable X is said to follow normal distribution with…

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A: Given that, For a standard normal distribution, X follows Normal distribution with mean 0 and…

Q: For a standard normal curve, find the probability a value has a z-score less than -2.

A: Standardized z-score:   The standardized z-score represents the number of standard deviations the…

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A: Here, n = 16

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A: Given,   Mean = 63.6 Standard deviation = 2.5 Sample size = 100   The objective is to find the…

Q: Given a standard normal distribution (with a mean of 0 and a standard deviation of 1) what is the…

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Q: A normal distribution has a mean of 211 and standard deviation of 13. Find the probability that a…

A: As per guidelines we will only answer first three subparts, please repost other subparts for more…

Q: A random sample of 25 observations yield a mean of 106 and a standard deviation of 12. Find the…

A: From the given information,Sample size 25, mean 106 and standard deviation 12

Q: Assume that adults have IQ scores that are normally distributed with a mean μ=100 and a standard…

A: Given μ = 100and  standard devaition (σ) = 20we need to calculate P( 89 < X < 111)

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A: Z = x-μσ~N(0,1)

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A: Mean = 6.5 Standard deviation = 1

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A: According to our guidelines we can answer the first question and rest can be reposted. Given that,…

Q: Assume that adults have IQ scores that are normally distributed with a mean of μ=100and a standard…

A: From the provided information, Mean (µ) = 100 Standard deviation (σ) = 20 Let X be a random variable…

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A: Mean = 107 Standard deviation = 14

Q: Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a standard…

A: Given : Assume that adults have IQ scores that are normally distributed with a mean of μ=100 and a…

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A: Let , X→N(μ=55 , σ=6) , n=16 Our aim is to the probability of selecting a sample of n=16 scores with…

Q: Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard…

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Q: Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard…

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A: Givenmean(μ)=60.0standard deviation(σ)=4.0

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

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A: A normal distribution has a mean of µ = 40 with σ = 8.

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Q: Assume a random variable X has a normal distribution with mean 500 and standard deviation 15. Find…

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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!