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mean household size in the United States in 2004 was 2.3 people, Statistics










































According to the Energy Information Administration, the mean household size in the United States in 2004 was 2.3 people with a standard deviation of 1.4. All possible samples of size 100 are randomly sampled from the population of US households.
a) What is the name of the sampling distribution?
b) Determine the mean and standard deviation of the sampling distribution. (use the correct name and symbol for each)
c) What is the probability that a random sample of 100 households selected from the population will have a mean household size of 1.5 or less?

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Dec 04, 2011
Statistics
by: Staff



Question:

According to the Energy Information Administration, the mean household size in the United States in 2004 was 2.3 people with a standard deviation of 1.4. All possible samples of size 100 are randomly sampled from the population of US households.

a) What is the name of the sampling distribution?
b) Determine the mean and standard deviation of the sampling distribution. (use the correct name and symbol for each)
c) What is the probability that a random sample of 100 households selected from the population will have a mean household size of 1.5 or less?



Answer:

According to the Energy Information Administration, the mean household size in the United States in 2004 was 2.3 people with a standard deviation of 1.4.

All possible samples of size 100 are randomly sampled from the population of US households.

a) What is the name of the sampling distribution?

The sampling distribution is the probability distribution (there are many, many types of probability distributions).

In this case it appears to be a normal distribution


b) Determine the mean and standard deviation of the sampling distribution. (use the correct name and symbol for each)

mean for sampling distribution: x̄, x-bar

x̄ = 2.3



standard deviation for sampling distribution: s, standard error

s = 1.4

(mean for entire population: μ, mu)
(standard deviation for entire population: σ, sigma)




c) What is the probability that a random sample of 100 households selected from the population will have a mean household size of 1.5 or less?

(2.3 people per household sampling mean - 1.5 people per household)/( standard deviation for sampling distribution of 1.4)

= (2.3 - 1.5 )/(1.4)

= 0.571429 standard deviations below the sample mean

Probability from z-table: 0.7157

Probability of persons per household being 1.5 or less:

1 - 0.7157 = 0.2843

The final answer to c) is: 28.43%.



I used the following z table

(1) Click the following link to VIEW the z table; or (2A) highlight and copy the link, then (2B) paste the link into your browser Address bar & press enter:

Use the Backspace key to return to this page:

http://www.solving-math-problems.com/images/Statistics-Probability-z-table-2011-12-04-01.png



Thanks for writing.

Staff
www.solving-math-problems.com



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