![loll9416](/avatars/37685.jpg)
loll9416
20.02.2020 •
Mathematics
4. Household size in the United States has a mean of 2.6 people and standard deviation of 1.4 people.However this distribution is skewed right as the smallest possible value is a household of 1 person butthe largest households can be very large indeed.(a) Suppose one household in the US is to be randomly selected. Can you calculate the probabilitythat the household size is higher than 4? If yes, calculate it; if no, explain why not.(b) Suppose 120 households are randomly selected and the average values in the sample is calculated.What is the expected value of mean size in the sample of 120 households?(c) Suppose 120 households are randomly selected and the average values in the sample is calculated.What is the standard deviation of mean size in the sample of 120 households?(d) What is the probability that the mean size of a random sample of 120 households is more than 3?
Solved
Show answers
More tips
- F Family and Home Tender Care for Your Parquet: Is it Possible to Clean Parquet?...
- S Society and Politics Is It Fact or Fiction? Let s Talk About Anton Chekhov s Pseudonym...
- S Sport Playing Bowling: Rules and Advice for Novices...
- C Computers and Internet How to Properly Repartition a Hard Drive?...
- A Auto and Moto What Is the Cost of Customs Clearance for a Car in Russia?...
- L Leisure and Entertainment Should You Buy a Ceramic Knife?...
- C Computers and Internet How to easily and quickly disable Firebug in Gmail and Google Docs...
- G Goods and services How to sew a ribbon: Tips for beginners...
- F Food and Cooking How to Make Mayonnaise at Home? Secrets of Homemade Mayonnaise...
- C Computers and Internet Which Phone is Best for Internet Surfing?...
Answers on questions: Mathematics
- M Mathematics Which.statement is true regarding the graphed functions? O (0) = 2 and g(-2) =0 O f(0) = 4 and g(-2)=4 O (2) =0 and g(-2) =0 O f(-2) =0 and g(-2) =0...
- M Mathematics 4.4 + [4 × 1/4 + 8.6]...
- M Mathematics 5^3 x 15^20+ 3^9 = Mates only...
- M Mathematics Graph the rational function f(x)=(3x-1)/(x-5)...
- M Mathematics Which theorem(s) can you use to prove that the two triangles are congruent?...
- M Mathematics PLEASE HELP I WILL GIVE BRAINLIEST!!...
- M Mathematics Please help I don’t get it...
- M Mathematics Someone help me with this...
- M Mathematics Determine if each set of ordered pairs represents y as a function of x. (Could have multiple correct answers.) 1.){(-2, 1), (-3, 1), (-4, 1), (-5, 1); 2.){(1, -2), (1, -3), (1,...
- M Mathematics The average cost of a gallon of gas in January 2014 was $3.42 and was $2.36 in December 2014. What was the percent change in the average cost of a gallon of gas in 2014? Round...
Ответ:
a) Cannot calculate, because the population is not normal.
b) 2.6 people
c) 0.1278 people
d) 0.9% probability that the mean size of a random sample of 120 households is more than 3.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit theorem
The Central Limit Theorem estabilishes that, for a random variable X, with mean
and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation ![s = \frac{\sigma}{\sqrt{n}}](/tpl/images/0517/7484/a95e6.png)
In this problem, we have that:
(a) Suppose one household in the US is to be randomly selected. Can you calculate the probabilitythat the household size is higher than 4? If yes, calculate it; if no, explain why not.
The population is not normal, so we cannot use the z-score formula to find this probability. So we cannot calculate this probability.
(b) Suppose 120 households are randomly selected and the average values in the sample is calculated.What is the expected value of mean size in the sample of 120 households?
By the Central Limit Theorem, we have that the mean is the same as the mean of the population, that is, 2.6 people.
(c) Suppose 120 households are randomly selected and the average values in the sample is calculated.What is the standard deviation of mean size in the sample of 120 households?
By the Central Limit Theorem
(d) What is the probability that the mean size of a random sample of 120 households is more than 3?
This is 1 subtracted by the pvalue of Z when X = 3. So
By the Central Limit Theorem
1 - 0.9991 = 0.0009
0.9% probability that the mean size of a random sample of 120 households is more than 3.
Ответ:
3g^2 = 30+9g