![Ary10113](/avatars/36394.jpg)
Ary10113
28.05.2020 •
Mathematics
According to a study done by the Gallup organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.82. Suppose a random sample of 100 Americans is asked the question "Are you satisfied with the way things are going in your life?" What is the probability the proportion of people who answer yes exceeds 0.85? Would it be unusual for a survey of 100 Americans to reveal that 75 or fewer are satisfiedwith the way things are going in their life?
Solved
Show answers
More tips
- A Animals and plants How to Store Carrots: Tips for Homeowners...
- L Legal consultation Juvenile Justice: Who Needs It?...
- F Family and Home How to Choose the Best Diapers for Your Baby?...
- F Family and Home Parquet or laminate, which is better?...
- L Leisure and Entertainment How to Properly Wind Fishing Line onto a Reel?...
- L Leisure and Entertainment How to Make a Paper Boat in Simple Steps...
- T Travel and tourism Maldives Adventures: What is the Best Season to Visit the Luxurious Beaches?...
- H Health and Medicine Kinesiology: What is it and How Does it Work?...
- O Other How to Choose the Best Answer to Your Question on The Grand Question ?...
- L Leisure and Entertainment History of International Women s Day: When Did the Celebration of March 8th Begin?...
Answers on questions: Mathematics
- M Mathematics I will give you brainliest if you help me with this...
- M Mathematics Use synthetic division to find the result when (x^3 - 2x^2 - 19x + 20) is divided by (x+4)...
- M Mathematics The Coffee Spot served several pastries this afternoon. Poppy seed muffins: 1 cinnamon rolls: 3 bran muffins: 2 apple fritters: 2 croissants: 2 Considering this data, how many...
- E English Select the example(s) of expository composition. personal letter directions recipe poem fairy tale instruction sheet mystery story atlas...
- S Social Studies Which group of people revolted against the Russianrevolutionary provisional government in 1917?...
Ответ:
0.217
Yes quite unusual ( See explanation )
Step-by-step explanation:
Solution:-
- Denote among population ( P ) of the proportion of Americans who are satisfied with flow of their lives are p = 0.82.
- A random sample of n = 100 Americans were asked whether they are satisfied with the way things are going in your life.
- The sampling distribution of population proportion will be checked for normality as follows:
n = 100 , p^ = 0.82
- The requirements of normal distribution of sample proportion distribution:
n*p^ & n( 1 - p^ ) ≥ 10
n*p^*( 1 - p^ ) ≥ 10
- Verify the assumption of sample proportion to be normally distributed:
n*p^ = 100*0.82 = 82 ≥ 10
n*( 1 - p^ ) = 100*( 1 - 0.82 ) = 18 ≥ 10
n*p*( 1 - p^ ) = 100*0.82*( 1 - 0.82 ) = 14.76 ≥ 10
- Therefore, we can assume the sample proportion to be normally distributed as per Central Limit Theorem i.e sample is sufficiently large.
- Normal distribution of population proportion ( P ) is defined by two parameters that are defined as:
P ~ Norm ( μ_p , σ_p^2 )
Where,
μ_p: The mean of proportion
σ_p: The standard deviation of proportion
- The parameters for normally distributed sample proportion will be estimated using point estimation and point standard error estimation of sample population distribution.
Estimation:
μ_p = sample proportion = p^ = 0.82
σ_p =
= 0.03842
Hence,
P ~ Norm ( 0.82 , 0.03842^2 )
- The probability of proportion of people who answered yes to the survey question is greater than 0.85.
- We are to compute the probability of p ( P > 0.85 ) using the normal sample distribution of ( P ) determined above:
- The Z-score for the limiting value is:
Z = ( P - μ_p ) / σ_p
Z = ( 0.85 - 0.82 ) / 0.03842
Z = 0.78084
- Now using standard normal tables or normal calculator determine the corresponding probability:
p ( P > 0.85 ) = p ( Z > 0.78084 )
= 0.217439
The probability that at-least 85 people in the random sample of n = 100 Americans who answered " yes " to the survey question is 0.217.
- If x = 75 or fewer Americans say that they are satisfied with the way things are going in their life among a population of N = 100.
- The proportion ( P ) of the Americans that answered " yes " to the survey question:
P = x / N
P = 75 / 100 = 0.75
- Now we will compare the population proportion ( P ≤ 0.75 ) against the sampling distribution of ( P ). Compute the Z-score of the limiting value:
Z = ( P - μ_p ) / σ_p
Z = ( 0.75 - 0.82 ) / 0.03842
Z = -1.82196
- Now using standard normal tables or normal calculator determine the corresponding probability:
p ( P ≤ 0.75 ) = p ( Z ≤ -1.82196 )
= 0.03422543
This means that about 3.4 out of 100 random samples of size 100 will result in 75% or lower are satisfied with their life if the population proportion of Americans who are satisfied with their life is 0.82. Hence, p ( P < 0.75 ) = 3 is quite unusual from a survey of 100 Americans to show that less than 75% answered yes to the posed question.
Ответ:
3279.82 cubic inches
53746.66 cm³
53.75 liters
Step-by-step explanation:
I hope this helps u! :D