Suppose a random variable X is best described by a normal distribution with =60 and et=14 Find the 2-score that corresponds to the value X = 96 36.1O

Q: A given distribution has a population mean, μ, of 134 and a population standard deviation, σ, of 7.…

A:

Q: For a sample of n = 30 scores, a score that is 6 points above the mean has a z-score of z = 1.50.…

A: For a sample of n = 30 scores, a score that is 6 points above the mean has a z-score of z = 1.50.

Q: A population forms a normal distribution with a mean of 85 and a standard deviation of 24 compute…

A: From the provided information, Mean (µ) = 85 Standard deviation (σ) = 24 X~N (85, 24)

Q: Given a normal distribution with a mean of 150, and a standard deviation of 7.5, find the value of a…

A: Consider that the mean and standard deviation of a random variable X are µ and σ, respectively.…

Q: a normal distribution has a mean of 60 with a standard deviation of 8. for this population, which is…

A: Solution

Q: What z-score would be associated with the value x = 124?

A: Given that Mean = 133 SD = 6 And the value is X = 124

Q: A given distribution has a population mean, μ, of 121 and a population standard deviation, σ, of 7.…

A:

Q: From a normal distribution with μ = 80 and σ = 8, what proportion of the curve lies at X ≥ 90?

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Q: A normal distribution has a mean of 20 and a standard deviation of 4. Determine the z-score for the…

A: Given that a normal distribution has a mean of 20 and a standard deviation of 4.  We need to…

Q: If X has a normal distribution of a mean of 70 and a standard deviation of 10, then the area under…

A:

Q: A given distribution has a population mean, μ, of 114 and a population standard deviation, σ, of 12.…

A:

Q: A z-score of −1 tells us that a score fell one standard deviation below the mean in a group of…

A: Empirical rule: For a normal distribution, the approximate values that fall in the specified…

Q: A given distribution has a population mean, μ, of 113 and a population standard deviation, σ, of 6.…

A: A given distribution has; a population mean(μ)=113 and a population standard deviation(σ)=6 find…

Q: A distribution is given as X ~ U(0, 12). What is the theoretical standard deviation?

A: concepts and reasonuniform distribution is a continuous probability distribution.it is defined…

Q: In a certain factory of rags, the time it takes for the workers to finish one rag is normally…

A: Solution: Let X be the time it takes for the workers to finish one rag. From the given information,…

Q: Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1. If…

A: Obtain the value of “a” if P(–a < z < a) = 0.4314. The value of “a” is obtained below as…

Q: A normal distribution has a mean of µ = 40 with σ = 10. If a vertical line is drawn through the…

A: Given a normal distribution with mean = 40Standard deviation = 10The Z score for any data point X is…

Q: A given distribution has a population mean, μ, of 150 and a population standard deviation, σ, of 6.…

A: Distributions are of 2 types, discrete and continuous. A normal distribution is a continuous…

Q: A given distribution has a population mean, μ, of 117 and a population standard deviation, σ, of 6.…

A: Given data, Mean (μ)=117 sd(σ)=6 If x=172 z=?

Q: suppose the random variable X has a normal distribution with a mean of 10 and a variance of 16…

A: Given information: X is a random variable follows normal distribution. That means,

Q: A score that is 6 points below the mean corresponds to a z-score of z = -2.00. What is the…

A: Given: z-score = -2.00 Formula: Where,

Q: Suppose that the average number of hurricanes heading to RGV is 32 per year witha standard deviation…

A: It is given that the, Hurricanes heading follows the normal distribution with the average number of…

Q: For a random sample of 9 women, the average resting pulse rate is x-bar = 76 beats per minute, and…

A:

Q: A normal distribution has a mean of µ = 30 with σ = 5. If a vertical line is drawn through the…

A: the PDF of normal distribution is = 1/σ * √2π * e ^ -(x-u)^2/ 2σ^2standard normal distribution is a…

Q: Sketch a normal distribution/bell curve with a mean of 60 and a standard deviation of 20.  What…

A: Given that  X~Normal( μ=60 , σ=20 )

Q: A sample of n = 5 scores has Σ X = 20 and Σ X2 = 180. For this sample, what is the value of the…

A:

Q: A score that is 9 points above the mean corresponds to a z-score of z = 1.50. What is the population…

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Q: Assume the random variable X is normally distributed with a mean of 50 and a standard deviation of…

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Q: A normal distribution has a mean of μ= 54 and a standard deviation of σ=6 What is the probability of…

A: The sample size is, n = 36 The values of mean and standard deviation of the sampling distribution…

Q: Suppose that the weights of adult males have a mean of 60kls and standard deviation of 18 kg.…

A: Given,mean(μ)=60standard deviation(σ)=18 Sample size(n)=40

Q: For a random sample of 9 women, the average resting pulse rate is x̅ = 76 beats per minute, and the…

A: Given: Sample size (n) = 9 Sample mean x¯=76 Sample standard deviation (s) = 5

Q: A normal distribution has a mean of 54, and a sttandard deviation of 6. What is the probability of…

A:

Q: Suppose a normal distribution has a mean of 50 and a standard deviation of 3. What is P(xs 53)?

A:

Q: Suppose x is a value in a normal distribution, with a mean of 12, and standard deviation of 4, What…

A: Given: x=4μ=12σ=4 The z score of x=4 is obtained as follows: Z=x-μσ=4-124=-84=-2 Thus, the z-score…

Q: If x is normally distributed with a mean of 5 and standard deviation of 2, find the P(x>8).

A:

Q: A population forms a normal distribution with a mean of 85 and a standard deviation of 24 compute…

A: The mean is 85 and the standard deviation is 24.

Q: A given distribution has a population mean, μ, of 144 and a population standard deviation, σ, of 9.…

A: Solution: Let X be the random variable. From the given information, X has a population mean µ=144…

Q: Suppose that blood chloride concentration (denoted by X) (mmol/L) has a normal distribution with…

A: The Z-score of a random variable X is defined as follows: Z = (X – µ)/σ. Here, µ and σ are the mean…

Q: distributed, with mean μ=55 and standard deviation σ=4. Find the 6th percentile

A: We have given that, Population mean (μ) = 55 and standard deviation (σ) = 4 Then,  We will find the…

Q: A given distribution has a population mean, μ, of 131 and a population standard deviation, σ, of 11.…

A:

Q: A given distribution has a population mean, μ, of 144 and a population standard deviation, σ, of 12.…

A: A given distribution has a population mean, μ, of 144 and a population standard deviation, σ, of 12.…

Q: A machine produces glass with a nominal thickness of 4mm. In fact the thickness is a Normal random…

A: Given,mean(μ)=4.168 mmstandard deviation(σ)=0.12mm

Q: The standard deviation of a normal random variable X is $50 . Given that P(X ≤ $40) = .25, what is…

A: Given data,σ=50x=40P(X ≤ $40) = .25μ=?

Q: suppose the random variable X has a normal distribution with a mean of 10 and a variance of 16…

A: Given: The random variable X is normally distributed. The population mean is given as:…

Q: A given distribution has a population mean, μ, of 142 and a population standard deviation, σ, of 10.…

A: It is given that the mean (µ) is 142 and the standard deviation (σ) is 10 and score, x is 110.

Q: "suppose that a random sample of size 20 is taken from a normal distribution with unknown variance…

A: Given: n=20 μ=Unknownx=10σ2=1Andμ(Posterior)=15σ(Posterior)=0.1

Q: Assume the scores on a standardized test are known to follow a bell-shaped distribution with a mean…

A: Here,  Sample size =1250 Mean=90 Variance =9 Standard deviation =3 Empirical rule: 68% of the data…

Q: Given a normal distribution with a mean of 130, and a standard deviation of 4.5, find the value of a…

A: Z-score corresponding to a normal variable value X is      (X-mu)/sigma Where,      X = normal…

Q: A given distribution has a population mean, μ, of 144 and a population standard deviation, σ, of 15.…

A:

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!