Question

1. In each case, identify the relevant sampling distribution (if possible), and justify your answer.

(a) House prices have a positively-skewed distribution. Suppose Perth house values have a mean price of $650,000 with a standard deviation of $450,000. What is the distribution of the average price of 45 randomly-selected Perth houses?

(b) Assume that birthdays are uniformly distributed over a calendar year.If X is the day- number of birthdays (i.e., X varies from 1 to 365, ignoring leap-years), then μX = 183 and σX = 105.37. What is the distribution of in samples of 20 randomly-selected people?

(c) In a rural adult population in northern Ghana, systolic blood pressure is roughly normally distributed with μ = 124.25 mm Hg and σ = 18.67 mm Hg. What sampling distribution is relevant to the average systolic blood pressure in a sample of 15 people from this population?

Answer 1

(a)

Here we have

According to central limit theorem, sampling distribution of the average price of 45 randomly-selected Perth houses will be approxiamtely normal distribution with mean

And standard deviation

(b)

The distibution of day- number in samples will also follow uniform distribution because sample size is less than 30. We cannot apply central limit theorem.

(c)

Here sample size is small but it is given that population is normally distributed.

According to central limit theorem, sampling distribution of the average systolic blood pressure in a sample of 15 people from this population will be approxiamtely normal distribution with mean

And standard deviation