How to find Standard Deviation, given Mean and Cumulative Normal Distribution?
The question specifically:
If X ∼ N(20, σ2) and Pr(X ≥ 19) = 0.7, find the standard deviation, σ.
I just don't quite understand how I can find the SD here?
I assume I need to find variance, and as such an expected value, but how might I go about this without a table of values?
probability statistics discrete-mathematics normal-distribution standard-deviation
asked Nov 22 at 13:37
Sam MacLennan
1
add a comment |
The question specifically:
If X ∼ N(20, σ2) and Pr(X ≥ 19) = 0.7, find the standard deviation, σ.
I just don't quite understand how I can find the SD here?
I assume I need to find variance, and as such an expected value, but how might I go about this without a table of values?
probability statistics discrete-mathematics normal-distribution standard-deviation
asked Nov 22 at 13:37
Sam MacLennan
1
1
Well you do need a table of values to solve $Phi(1/sigma)=0.7$, which is what you get rewriting the probability $P(Xge 19)$ in terms of the standard normal cdf $Phi$.
– StubbornAtom
Nov 22 at 13:48
add a comment |
The question specifically:
If X ∼ N(20, σ2) and Pr(X ≥ 19) = 0.7, find the standard deviation, σ.
I just don't quite understand how I can find the SD here?
I assume I need to find variance, and as such an expected value, but how might I go about this without a table of values?
probability statistics discrete-mathematics normal-distribution standard-deviation
asked Nov 22 at 13:37
Sam MacLennan
1
The question specifically:
If X ∼ N(20, σ2) and Pr(X ≥ 19) = 0.7, find the standard deviation, σ.
I just don't quite understand how I can find the SD here?
I assume I need to find variance, and as such an expected value, but how might I go about this without a table of values?
probability statistics discrete-mathematics normal-distribution standard-deviation
probability statistics discrete-mathematics normal-distribution standard-deviation
asked Nov 22 at 13:37
Sam MacLennan
1
asked Nov 22 at 13:37
Sam MacLennan
1
asked Nov 22 at 13:37
Sam MacLennan
1
asked Nov 22 at 13:37
Sam MacLennan
1
asked Nov 22 at 13:37
Sam MacLennan
1
1
1
Well you do need a table of values to solve $Phi(1/sigma)=0.7$, which is what you get rewriting the probability $P(Xge 19)$ in terms of the standard normal cdf $Phi$.
– StubbornAtom
Nov 22 at 13:48
add a comment |
1
Well you do need a table of values to solve $Phi(1/sigma)=0.7$, which is what you get rewriting the probability $P(Xge 19)$ in terms of the standard normal cdf $Phi$.
– StubbornAtom
Nov 22 at 13:48
1
1
Well you do need a table of values to solve $Phi(1/sigma)=0.7$, which is what you get rewriting the probability $P(Xge 19)$ in terms of the standard normal cdf $Phi$.
– StubbornAtom
Nov 22 at 13:48
Well you do need a table of values to solve $Phi(1/sigma)=0.7$, which is what you get rewriting the probability $P(Xge 19)$ in terms of the standard normal cdf $Phi$.
– StubbornAtom
Nov 22 at 13:48
add a comment |
1 Answer
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Following @StubbornAtom's Comment of a couple of days ago, this suggests how to find the answer. Make sure you can use methods and tables in your
text to get the answer.
To start:
$$P(X ge 19) = Pleft(frac{X-mu}{sigma} ge frac{19-20}{sigma} = -frac 1 sigmaright) = P(Z ge -1/sigma) = .07.$$
But from standard normal tables or from software you know that $P(Z ge -0.5255) = 0.7,$ whers $Z sim mathsf{Norm}(0,1).$ Do you know how to use a printed table to get close to this result?
Then finally, how do you find $sigma?$
Computations in R statistical software:
qnorm(.3)
[1] -0.5244005 # c = -0.5244 has P(Z < c) = 0.3
1 - pnorm(19, 20, 1.907)
[1] 0.6999942 # P(X > 19) = 0.7 if X ~ NORM(mu=20, sigma=1.907)
answered Nov 24 at 22:56
BruceET
35.1k71440
add a comment |
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1 Answer
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1 Answer
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Following @StubbornAtom's Comment of a couple of days ago, this suggests how to find the answer. Make sure you can use methods and tables in your
text to get the answer.
To start:
$$P(X ge 19) = Pleft(frac{X-mu}{sigma} ge frac{19-20}{sigma} = -frac 1 sigmaright) = P(Z ge -1/sigma) = .07.$$
But from standard normal tables or from software you know that $P(Z ge -0.5255) = 0.7,$ whers $Z sim mathsf{Norm}(0,1).$ Do you know how to use a printed table to get close to this result?
Then finally, how do you find $sigma?$
Computations in R statistical software:
qnorm(.3)
[1] -0.5244005 # c = -0.5244 has P(Z < c) = 0.3
1 - pnorm(19, 20, 1.907)
[1] 0.6999942 # P(X > 19) = 0.7 if X ~ NORM(mu=20, sigma=1.907)
answered Nov 24 at 22:56
BruceET
35.1k71440
add a comment |
Following @StubbornAtom's Comment of a couple of days ago, this suggests how to find the answer. Make sure you can use methods and tables in your
text to get the answer.
To start:
$$P(X ge 19) = Pleft(frac{X-mu}{sigma} ge frac{19-20}{sigma} = -frac 1 sigmaright) = P(Z ge -1/sigma) = .07.$$
But from standard normal tables or from software you know that $P(Z ge -0.5255) = 0.7,$ whers $Z sim mathsf{Norm}(0,1).$ Do you know how to use a printed table to get close to this result?
Then finally, how do you find $sigma?$
Computations in R statistical software:
qnorm(.3)
[1] -0.5244005 # c = -0.5244 has P(Z < c) = 0.3
1 - pnorm(19, 20, 1.907)
[1] 0.6999942 # P(X > 19) = 0.7 if X ~ NORM(mu=20, sigma=1.907)
answered Nov 24 at 22:56
BruceET
35.1k71440
add a comment |
Following @StubbornAtom's Comment of a couple of days ago, this suggests how to find the answer. Make sure you can use methods and tables in your
text to get the answer.
To start:
$$P(X ge 19) = Pleft(frac{X-mu}{sigma} ge frac{19-20}{sigma} = -frac 1 sigmaright) = P(Z ge -1/sigma) = .07.$$
But from standard normal tables or from software you know that $P(Z ge -0.5255) = 0.7,$ whers $Z sim mathsf{Norm}(0,1).$ Do you know how to use a printed table to get close to this result?
Then finally, how do you find $sigma?$
Computations in R statistical software:
qnorm(.3)
[1] -0.5244005 # c = -0.5244 has P(Z < c) = 0.3
1 - pnorm(19, 20, 1.907)
[1] 0.6999942 # P(X > 19) = 0.7 if X ~ NORM(mu=20, sigma=1.907)
answered Nov 24 at 22:56
BruceET
35.1k71440
Following @StubbornAtom's Comment of a couple of days ago, this suggests how to find the answer. Make sure you can use methods and tables in your
text to get the answer.
To start:
$$P(X ge 19) = Pleft(frac{X-mu}{sigma} ge frac{19-20}{sigma} = -frac 1 sigmaright) = P(Z ge -1/sigma) = .07.$$
But from standard normal tables or from software you know that $P(Z ge -0.5255) = 0.7,$ whers $Z sim mathsf{Norm}(0,1).$ Do you know how to use a printed table to get close to this result?
Then finally, how do you find $sigma?$
Computations in R statistical software:
qnorm(.3)
[1] -0.5244005 # c = -0.5244 has P(Z < c) = 0.3
1 - pnorm(19, 20, 1.907)
[1] 0.6999942 # P(X > 19) = 0.7 if X ~ NORM(mu=20, sigma=1.907)
answered Nov 24 at 22:56
BruceET
35.1k71440
edited Nov 24 at 23:07
answered Nov 24 at 22:56
BruceET
35.1k71440
answered Nov 24 at 22:56
BruceET
35.1k71440
answered Nov 24 at 22:56
BruceET
35.1k71440
35.1k71440
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Well you do need a table of values to solve $Phi(1/sigma)=0.7$, which is what you get rewriting the probability $P(Xge 19)$ in terms of the standard normal cdf $Phi$.
– StubbornAtom
Nov 22 at 13:48