MATH SOLVE

4 months ago

Q:
# 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.

Accepted Solution

A:

Answer: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 muc) the standard deviation σx of the sampling distribution approach to σ/√nd) The means are the same. . The standard deviations are σ / √50 and σ / √100, respectively.