calculate minimum sample number
i have assignment to solve the following problem,
The height of a person is a random variable with variance ≤5 inches2. According to Mr. Chebyshev, how many people do we need to sample to ensure that the sample mean is at most 1 inch away from the distribution mean with probability ≥95%?
i tried solve the problem by first apply weak law of large numbers as follows
P(|x-u|>= a) <= variance/a.n where X is sample mean and n is the sample size.
then, by applying WLLN
P(|X-u| <= 1) <= 1 - 0.95, means variance/1.n = 0.05. and n = 500
however, obtained n=500 is inches number but question requested number of persons. how can i find number of persons given that i correctly calculated number of inches 500.
probability-distributions
edited Nov 26 at 15:01
Ethan Bolker
41.2k547108
asked Nov 26 at 15:00
Nour
254
add a comment |
i have assignment to solve the following problem,
The height of a person is a random variable with variance ≤5 inches2. According to Mr. Chebyshev, how many people do we need to sample to ensure that the sample mean is at most 1 inch away from the distribution mean with probability ≥95%?
i tried solve the problem by first apply weak law of large numbers as follows
P(|x-u|>= a) <= variance/a.n where X is sample mean and n is the sample size.
then, by applying WLLN
P(|X-u| <= 1) <= 1 - 0.95, means variance/1.n = 0.05. and n = 500
however, obtained n=500 is inches number but question requested number of persons. how can i find number of persons given that i correctly calculated number of inches 500.
probability-distributions
edited Nov 26 at 15:01
Ethan Bolker
41.2k547108
asked Nov 26 at 15:00
Nour
254
We use a type of $LaTeX$ called MathJax here. Please search for a tutorial on it :)
– Shaun
Nov 26 at 15:13
No idea where you get “$n=500$ is the number of inches” from. It has nothing to do with inches... it is the sample size. On a more minor note you seem to have forgotten to plug in the variance as $5$: it should be $n=100.$
– spaceisdarkgreen
Nov 26 at 15:23
your answer is correct Shaun it is n=100 thank you very much, actually i got n=500 when i plug variance as 25, i did so as i got confused due to number "2" after word "inches" in the question, i though it is power of 2. thanks a lot again.
– Nour
Nov 26 at 15:49
add a comment |
i have assignment to solve the following problem,
The height of a person is a random variable with variance ≤5 inches2. According to Mr. Chebyshev, how many people do we need to sample to ensure that the sample mean is at most 1 inch away from the distribution mean with probability ≥95%?
i tried solve the problem by first apply weak law of large numbers as follows
P(|x-u|>= a) <= variance/a.n where X is sample mean and n is the sample size.
then, by applying WLLN
P(|X-u| <= 1) <= 1 - 0.95, means variance/1.n = 0.05. and n = 500
however, obtained n=500 is inches number but question requested number of persons. how can i find number of persons given that i correctly calculated number of inches 500.
probability-distributions
edited Nov 26 at 15:01
Ethan Bolker
41.2k547108
asked Nov 26 at 15:00
Nour
254
i have assignment to solve the following problem,
The height of a person is a random variable with variance ≤5 inches2. According to Mr. Chebyshev, how many people do we need to sample to ensure that the sample mean is at most 1 inch away from the distribution mean with probability ≥95%?
i tried solve the problem by first apply weak law of large numbers as follows
P(|x-u|>= a) <= variance/a.n where X is sample mean and n is the sample size.
then, by applying WLLN
P(|X-u| <= 1) <= 1 - 0.95, means variance/1.n = 0.05. and n = 500
however, obtained n=500 is inches number but question requested number of persons. how can i find number of persons given that i correctly calculated number of inches 500.
probability-distributions
probability-distributions
edited Nov 26 at 15:01
Ethan Bolker
41.2k547108
asked Nov 26 at 15:00
Nour
254
edited Nov 26 at 15:01
Ethan Bolker
41.2k547108
asked Nov 26 at 15:00
Nour
254
edited Nov 26 at 15:01
Ethan Bolker
41.2k547108
edited Nov 26 at 15:01
Ethan Bolker
41.2k547108
edited Nov 26 at 15:01
Ethan Bolker
41.2k547108
41.2k547108
asked Nov 26 at 15:00
Nour
254
asked Nov 26 at 15:00
Nour
254
asked Nov 26 at 15:00
Nour
254
254
We use a type of $LaTeX$ called MathJax here. Please search for a tutorial on it :)
– Shaun
Nov 26 at 15:13
No idea where you get “$n=500$ is the number of inches” from. It has nothing to do with inches... it is the sample size. On a more minor note you seem to have forgotten to plug in the variance as $5$: it should be $n=100.$
– spaceisdarkgreen
Nov 26 at 15:23
your answer is correct Shaun it is n=100 thank you very much, actually i got n=500 when i plug variance as 25, i did so as i got confused due to number "2" after word "inches" in the question, i though it is power of 2. thanks a lot again.
– Nour
Nov 26 at 15:49
add a comment |
We use a type of $LaTeX$ called MathJax here. Please search for a tutorial on it :)
– Shaun
Nov 26 at 15:13
No idea where you get “$n=500$ is the number of inches” from. It has nothing to do with inches... it is the sample size. On a more minor note you seem to have forgotten to plug in the variance as $5$: it should be $n=100.$
– spaceisdarkgreen
Nov 26 at 15:23
your answer is correct Shaun it is n=100 thank you very much, actually i got n=500 when i plug variance as 25, i did so as i got confused due to number "2" after word "inches" in the question, i though it is power of 2. thanks a lot again.
– Nour
Nov 26 at 15:49
We use a type of $LaTeX$ called MathJax here. Please search for a tutorial on it :)
– Shaun
Nov 26 at 15:13
We use a type of $LaTeX$ called MathJax here. Please search for a tutorial on it :)
– Shaun
Nov 26 at 15:13
No idea where you get “$n=500$ is the number of inches” from. It has nothing to do with inches... it is the sample size. On a more minor note you seem to have forgotten to plug in the variance as $5$: it should be $n=100.$
– spaceisdarkgreen
Nov 26 at 15:23
No idea where you get “$n=500$ is the number of inches” from. It has nothing to do with inches... it is the sample size. On a more minor note you seem to have forgotten to plug in the variance as $5$: it should be $n=100.$
– spaceisdarkgreen
Nov 26 at 15:23
your answer is correct Shaun it is n=100 thank you very much, actually i got n=500 when i plug variance as 25, i did so as i got confused due to number "2" after word "inches" in the question, i though it is power of 2. thanks a lot again.
– Nour
Nov 26 at 15:49
your answer is correct Shaun it is n=100 thank you very much, actually i got n=500 when i plug variance as 25, i did so as i got confused due to number "2" after word "inches" in the question, i though it is power of 2. thanks a lot again.
– Nour
Nov 26 at 15:49
add a comment |
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We use a type of $LaTeX$ called MathJax here. Please search for a tutorial on it :)
– Shaun
Nov 26 at 15:13
No idea where you get “$n=500$ is the number of inches” from. It has nothing to do with inches... it is the sample size. On a more minor note you seem to have forgotten to plug in the variance as $5$: it should be $n=100.$
– spaceisdarkgreen
Nov 26 at 15:23
your answer is correct Shaun it is n=100 thank you very much, actually i got n=500 when i plug variance as 25, i did so as i got confused due to number "2" after word "inches" in the question, i though it is power of 2. thanks a lot again.
– Nour
Nov 26 at 15:49