Answer:
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!!!
