How to find percentage given mean and standard deviation?
The speed limit on Union street is 40 km/h. Rachel and Joe measured the speed of passing vehicles over a period of time. They found the set of data to be normally distributed with a mean speed of 36 km/h and a standard deviation of 2 km/h.
What percentage of the vehicles passed on Union Street at speed greater than 40 km/h?
If μ=36 σ=2
Z=x-μ /σ
so Z=2
Z>2
R(2)=0,02275
So the percentage of the vehicles passed on Union Street at speed greater than 40 km/h is 2,28%
Is the first time that I try to solve this kind of exercise. Is this correct?
statistics standard-deviation means
asked Aug 5 '17 at 20:01
tuscantuscan
422
add a comment |
The speed limit on Union street is 40 km/h. Rachel and Joe measured the speed of passing vehicles over a period of time. They found the set of data to be normally distributed with a mean speed of 36 km/h and a standard deviation of 2 km/h.
What percentage of the vehicles passed on Union Street at speed greater than 40 km/h?
If μ=36 σ=2
Z=x-μ /σ
so Z=2
Z>2
R(2)=0,02275
So the percentage of the vehicles passed on Union Street at speed greater than 40 km/h is 2,28%
Is the first time that I try to solve this kind of exercise. Is this correct?
statistics standard-deviation means
asked Aug 5 '17 at 20:01
tuscantuscan
422
add a comment |
The speed limit on Union street is 40 km/h. Rachel and Joe measured the speed of passing vehicles over a period of time. They found the set of data to be normally distributed with a mean speed of 36 km/h and a standard deviation of 2 km/h.
What percentage of the vehicles passed on Union Street at speed greater than 40 km/h?
If μ=36 σ=2
Z=x-μ /σ
so Z=2
Z>2
R(2)=0,02275
So the percentage of the vehicles passed on Union Street at speed greater than 40 km/h is 2,28%
Is the first time that I try to solve this kind of exercise. Is this correct?
statistics standard-deviation means
asked Aug 5 '17 at 20:01
tuscantuscan
422
The speed limit on Union street is 40 km/h. Rachel and Joe measured the speed of passing vehicles over a period of time. They found the set of data to be normally distributed with a mean speed of 36 km/h and a standard deviation of 2 km/h.
What percentage of the vehicles passed on Union Street at speed greater than 40 km/h?
If μ=36 σ=2
Z=x-μ /σ
so Z=2
Z>2
R(2)=0,02275
So the percentage of the vehicles passed on Union Street at speed greater than 40 km/h is 2,28%
Is the first time that I try to solve this kind of exercise. Is this correct?
statistics standard-deviation means
statistics standard-deviation means
asked Aug 5 '17 at 20:01
tuscantuscan
422
asked Aug 5 '17 at 20:01
tuscantuscan
422
asked Aug 5 '17 at 20:01
tuscantuscan
422
asked Aug 5 '17 at 20:01
tuscantuscan
422
asked Aug 5 '17 at 20:01
tuscantuscan
422
422
add a comment |
add a comment |
1 Answer
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You have vehicle speeds $X sim mathsf{Norm}(mu = 36, sigma = 2)$ and
you seek
$$P(X > 40) = Pleft(frac{X - mu}{sigma} > frac{40-36}{2}right)
= P(Z > 2) = 0.02275,$$
where $Z$ has the standard normal distribution and the probability
can be found using printed normal tables or software.
You do not define what you mean by $R,$ but the numerical answer is OK.
Note: Using some kinds of statistical software you can skip the 'standardization
step' and get the answer directly. In R statistical software, for example,
you could use
1 - pnorm(40, 36, 2)
## 0.02275013
In Minitab 16 you can get $P(X le 40)$ and then subtract from $1.$
MTB > cdf 40;
SUBC> norm 36 2.
Cumulative Distribution Function
Normal with mean = 36 and standard deviation = 2
x P( X ≤ x )
40 0.977250
answered Aug 7 '17 at 4:52
BruceETBruceET
35.2k71440
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
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active
oldest
votes
You have vehicle speeds $X sim mathsf{Norm}(mu = 36, sigma = 2)$ and
you seek
$$P(X > 40) = Pleft(frac{X - mu}{sigma} > frac{40-36}{2}right)
= P(Z > 2) = 0.02275,$$
where $Z$ has the standard normal distribution and the probability
can be found using printed normal tables or software.
You do not define what you mean by $R,$ but the numerical answer is OK.
Note: Using some kinds of statistical software you can skip the 'standardization
step' and get the answer directly. In R statistical software, for example,
you could use
1 - pnorm(40, 36, 2)
## 0.02275013
In Minitab 16 you can get $P(X le 40)$ and then subtract from $1.$
MTB > cdf 40;
SUBC> norm 36 2.
Cumulative Distribution Function
Normal with mean = 36 and standard deviation = 2
x P( X ≤ x )
40 0.977250
answered Aug 7 '17 at 4:52
BruceETBruceET
35.2k71440
add a comment |
You have vehicle speeds $X sim mathsf{Norm}(mu = 36, sigma = 2)$ and
you seek
$$P(X > 40) = Pleft(frac{X - mu}{sigma} > frac{40-36}{2}right)
= P(Z > 2) = 0.02275,$$
where $Z$ has the standard normal distribution and the probability
can be found using printed normal tables or software.
You do not define what you mean by $R,$ but the numerical answer is OK.
Note: Using some kinds of statistical software you can skip the 'standardization
step' and get the answer directly. In R statistical software, for example,
you could use
1 - pnorm(40, 36, 2)
## 0.02275013
In Minitab 16 you can get $P(X le 40)$ and then subtract from $1.$
MTB > cdf 40;
SUBC> norm 36 2.
Cumulative Distribution Function
Normal with mean = 36 and standard deviation = 2
x P( X ≤ x )
40 0.977250
answered Aug 7 '17 at 4:52
BruceETBruceET
35.2k71440
add a comment |
You have vehicle speeds $X sim mathsf{Norm}(mu = 36, sigma = 2)$ and
you seek
$$P(X > 40) = Pleft(frac{X - mu}{sigma} > frac{40-36}{2}right)
= P(Z > 2) = 0.02275,$$
where $Z$ has the standard normal distribution and the probability
can be found using printed normal tables or software.
You do not define what you mean by $R,$ but the numerical answer is OK.
Note: Using some kinds of statistical software you can skip the 'standardization
step' and get the answer directly. In R statistical software, for example,
you could use
1 - pnorm(40, 36, 2)
## 0.02275013
In Minitab 16 you can get $P(X le 40)$ and then subtract from $1.$
MTB > cdf 40;
SUBC> norm 36 2.
Cumulative Distribution Function
Normal with mean = 36 and standard deviation = 2
x P( X ≤ x )
40 0.977250
answered Aug 7 '17 at 4:52
BruceETBruceET
35.2k71440
You have vehicle speeds $X sim mathsf{Norm}(mu = 36, sigma = 2)$ and
you seek
$$P(X > 40) = Pleft(frac{X - mu}{sigma} > frac{40-36}{2}right)
= P(Z > 2) = 0.02275,$$
where $Z$ has the standard normal distribution and the probability
can be found using printed normal tables or software.
You do not define what you mean by $R,$ but the numerical answer is OK.
Note: Using some kinds of statistical software you can skip the 'standardization
step' and get the answer directly. In R statistical software, for example,
you could use
1 - pnorm(40, 36, 2)
## 0.02275013
In Minitab 16 you can get $P(X le 40)$ and then subtract from $1.$
MTB > cdf 40;
SUBC> norm 36 2.
Cumulative Distribution Function
Normal with mean = 36 and standard deviation = 2
x P( X ≤ x )
40 0.977250
answered Aug 7 '17 at 4:52
BruceETBruceET
35.2k71440
edited Aug 7 '17 at 5:04
answered Aug 7 '17 at 4:52
BruceETBruceET
35.2k71440
answered Aug 7 '17 at 4:52
BruceETBruceET
35.2k71440
answered Aug 7 '17 at 4:52
BruceETBruceET
35.2k71440
35.2k71440
add a comment |
add a comment |
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