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? uniform distribution sampling distribution normal distribution binomial distribution (b) as the sample size becomes increasingly large, what value will the mean μx of the x distribution approach? μx μ μ/√n μ/n σ (c) what value will the standard deviation σx of the sampling distribution approach? σ/n σx σ/√n μ σ (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 means are the same. the standard deviations are the same. the standard deviations are σ / √50 and σ / √100, respectively. the standard deviations are μ / √50 and μ / √100, respectively. the standard deviations are σ / 50 and σ / 100, respectively.

Step-by-step explanation:

Given that X is a random variable representing the amount of sleep each adult in New York City got last night.

a) Normal distribution (by central limit theorem)

b) Sample mean will approach population mean mu

c) the standard deviation σx of the sampling distribution approach to σ/√n

d)  The means are the same.

. The standard deviations are σ / √50 and σ / √100, respectively.

a) As the sample size becomes increasingly large, the distribution approximates a normal distribution.

b) As the sample size becomes increasingly large, the mean of the sampling distribution, μₓ, approach as the population mean, μ.

σₓ

c) The standard deviation of the sampling distribution is given as

σₓ = (σ/√n)

d) Two sampling distributions with Sample size 50 and 100 have standard deviation of sampling distribution of (σ/√50) and (σ/√100) respectively.

Step-by-step explanation:

The Central limit theorem explains that sample distributions obtained from a population distribution (especially normally distributed ones) have distributions that approximate a normal distribution, a mean that is equal to the population mean and a standard deviation of sampling distribution given as the population standard deviation divided by square root of sample size.

a) Just like the Central limit theorem explains, as the sample size becomes increasingly large, the distribution approximates a normal distribution

b) And as the sample size becomes increasingly large, the mean of the sampling distribution, μₓ, approach as the population mean, μ.

c) The standard deviation of the sampling distribution is given as the population standard deviation divided by square root of sample size.

d) Using the formula given in (c) above, the standard deviation of sampling distribution of two sampling distributions with sample size 50 and 100 are (σ/√50) and (σ/√100) respectively.

Hope this Helps!!!

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for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.