SOLUTION: 1. A survey reports its results by stating that standard error of the mean to be is 20. The population standard deviation is 500. (i). How large is the sample used in this survey?

Question 1177196: 1. A survey reports its results by stating that standard error of the mean to be is 20. The population standard deviation is 500.
(i). How large is the sample used in this survey?
(ii). What is the probability that the sample mean will be within 25 of the population mean?
2(a). The time it takes a fire department to respond to a request for emergency aid has a mean of 14 minutes with standard deviation of 4 minutes. Suppose we randomly sample 50 emergency requests over a two-month period.
(i). State the sampling distribution of the sample mean, ̅x.
(ii). What is the probability that the sample mean will be 15 minutes or less?
(iii). What role does the Central Limit Theorem play in identifying this distribution?
(b). A population has a mean of 400 and a standard deviation of 50. The probability distribution of the population is unknown. A research study will use a simple random sample of either 10, 20, 35, or 50. items to collect data about the population.
(i). In which of these sample sizes will you be able to use the Normal probability distribution to describe the sampling distribution of the sample mean, ̅x. Explain.
(iii). Determine the standard error of the sampling distribution of ̅x for the instances where the Normal distribution would be appropriate.
(iii). What theorem would you appeal to for the justification of your answers in (i) and (ii). State it.

Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!


Hi

!.   = 20
i.  = (500/20)^2 = 625

ii. ME = =25
   25 = z*20
   z = 25/20 = 1.25  and P (z ≤  1.25) = .8944

2a.   
       1/SE = z =  1.7678  and P(z ≤  1.7678) = .9615
The central limit theorem states that whenever a random sample of size n is taken from any distribution with mean and variance, then the sample mean will be approximately normally distributed with mean and variance
 We are proceeding as if the distribution of this sample(size 50)..its mean will be approximately normally distributed.

Will let You finish up or repost your last question.
Site asks that there be one question per post.
Wish You the Best in your Studies.

RELATED QUESTIONS
A researcher reports survey results by stating that the standard error of the mean is 20. (answered by Theo)

A survey reports it results by starting that standard error of the mean to be is 20. The (answered by Theo)

i need your help this is statics questions 1.A restaurant tells its customers that the (answered by Boreal)

The standard deviation of a population is known to be 7.8. If the sample size is 85, what (answered by stanbon)

Given the population standard deviation equals 70, and the standard error of the mean... (answered by stanbon)

Scarlett and Heather, the owners of an upscale restaurant in Dayton, Ohio, want to study... (answered by Theo)

1) A population has a mean of μ = 50 and a standard deviation of σ= 12. For samples of (answered by Theo)

A sample of 10 observations is selected from a normal population for which the population (answered by stanbon)

An article in the San Jose Mercury News stated that students in the California state... (answered by Boreal)