Question

Help please !

Annual incomes are known to have a distribution that is skewed to the rnight instead of being normally dis sample of annual incomes. Can the distribution of incomes in that sample be approximated by a normal distibution because the sample is large? right instead of being normally distributed Assume that we cllect a large (n> 30) random Why or why not? Choose the correct answer below OA. Yes, the sample size is over 30, so the sample of incomes will be normally distnibuted O B. No, the sample means will be normally distributed, but the sample of incomes will be skewed to the right te of incomes is not normally distibuted, so the sample meas will not be normally distributed for any sample size O D. Nor unless more than 30 samples are collcted, the sample of ncomes vill not be normallydstributid Click to select your answer

Answer 1

Solution:-

(A) Yes, the sample size is over 30, so the samples of incomes will be normally distributed.

The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large (usually n > 30). If the population is normal, then the theorem holds true even for samples smaller than 30.