Question

The Central Limit Theorem implies that [Select the correct answers - There may be more than one correct answer. Negative marking will apply for incorrect selections.]

(a) All variables have bell-shaped sample data distributions if a random sample con- tains at least about 30 observations.

(b) Population distributions are normal whenever the population size is large.

(c) For large random samples, the sampling distribution of y ̄ is approximately normal, regardless of the shape of the population distribution.

(d) The sampling distribution looks more like the population distribution as the sam- ple size increases.

can you please explain with example

Answer 1

Ans:

Correct options are:

For large random samples, the sampling distribution of is approximately normal, regardless of the shape of the population distribution.

The sampling distribution looks more like the population distribution as the sam- ple size increases.

e.g.

The population of adult males has a mean salary of $29,500 with a standard deviation of $2500. If a sample of 100 men is taken, what is the probability their mean salaries will be less than $29,000?

samplinf distribution of sample means(y-bar):

mean=29500

standard deviation=2500/sqrt(100)=250

z=(29000-29500)/250

z=-2

P(z<-2)=0.0228