Question

Suppose we had found that the variable giving the amount of grant money raised by the charity in the last year follows a right skewed distribution with mean equal to $500,000 and standard deviation equal to $850,000. This is hypothetical. We did not actually measure the variable. We look at the average amount of grant money raised by 40 randomly sampled charities from the charity navigator website. 2. Describe the shape of the sampling distribution of the sample averages of size N- 40, a) What is the mean and standard deviation of the sampling distribution of the sample averages (also called the standard error of size c) 40? What is the probability that the sample average of these 40 charities is more than $490,000? Hint: Use the Excel calculator c)
please explain related concept in detail for better understansing.

Answer 1

Solution

'According to the Central Limit Theorem, if population is very large, if we perform random sampling and if the the size of the sample is equal to or greater than 30 (n> 30),  regardless of the shape and distribution of the population, the sampling distribution of sample mean will be normal. The value of the sample mean will be approximately equal to the Population mean, and standard deviation of the sample will be : (population std. dev.)/sqrt(n).

a.)Shape: Normal Distribution

b.)Mean(x̅)=μ=500,000

Standard Error=population Std. Dev/sqrt(n)

=850000/sqrt(40)

=134396.8

c.)P(x̅>490000)=1-P(x̅<490000)

=1-P(Z < (490000-500000)/134396.8)

=1-P(Z < -0.07)

=1-0.4721 (use excel function: =NORMSDIST(-0.07))

=0.5279