Let x be a random variable representing the amount of sleep each adult in New York City got last night. Consider a sampling distribution of sample means x.(a) As the sample size becomes increasingly large, what distribution does the x distribution approach?binomial distributionsampling distribution normal distributionuniform distribution (b) As the sample size becomes increasingly large, what value will the mean μx of the x distribution approach?μσ μ/nμ/√nμx (c) What value will the standard deviation σx of the sampling distribution approach?σ/√nσ μσ/nσx (d) How do the two x distributions for sample size n = 50 and n = 100 compare? (Select all that apply.)The standard deviations are μ / √50 and μ / √100, respectively.The standard deviations are μ / 50 and μ / 100, respectively.The standard deviations are σ / √50 and σ / √100, respectively.The standard deviations are σ / 50 and σ / 100, respectively.The standard deviations are the same.The means are the same.
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!
Let x be a random variable representing the amount of sleep each adult in New York City got last night. Consider a sampling distribution of sample means x.
(a) As the
binomial distribution
sampling
normal
uniform distribution
(b) As the sample size becomes increasingly large, what value will the
μ
σ
μ/n
μ/√n
μx
(c) What value will the standard deviation σx of the sampling distribution approach?
σ/√n
σ
μ
σ/n
σx
(d) How do the two x distributions for sample size n = 50 and n = 100 compare? (Select all that apply.)
The standard deviations are μ / √50 and μ / √100, respectively.
The standard deviations are μ / 50 and μ / 100, respectively.
The standard deviations are σ / √50 and σ / √100, respectively.
The standard deviations are σ / 50 and σ / 100, respectively.
The standard deviations are the same.
The means are the same.
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