Using P(X=n) in normal distribution questions.
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Firstly, I know you don't use $P(X=n)$ in normal distribution questions.
But I have a question where I'm kind of baffled on how to write the probability.
A scientist noted that 36% of temperature measurements were 4°C lower than the average.
I want to say I'd write $P(X<μ-4) = 0.36$ But it just doesn't make sense to me. I would instinctively write $P(X=μ-4) = 0.36$ because I'm looking at values where temperatures are exactly 4°C lower and not at least 4°C lower than the average. So where am I going wrong in understanding this?
probability proof-verification normal-distribution
asked Aug 9 at 23:51
Cheks Nweze
797
add a comment |Â
up vote
1
down vote
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Firstly, I know you don't use $P(X=n)$ in normal distribution questions.
But I have a question where I'm kind of baffled on how to write the probability.
A scientist noted that 36% of temperature measurements were 4°C lower than the average.
I want to say I'd write $P(X<μ-4) = 0.36$ But it just doesn't make sense to me. I would instinctively write $P(X=μ-4) = 0.36$ because I'm looking at values where temperatures are exactly 4°C lower and not at least 4°C lower than the average. So where am I going wrong in understanding this?
probability proof-verification normal-distribution
asked Aug 9 at 23:51
Cheks Nweze
797
1
The question is poorly stated. If $36%$ were exactly 4°C lower than the average, it certainly wouldn't be a normal distribution, because it wouldn't be continuous. It could be that what is meant is that $36%$ were at least 4°C lower, or perhaps that $36%$ were between $3.5$ and $4.5$ degrees lower.
– Robert Israel
Aug 10 at 0:05
I believe the correct interpretation is $$ Pr(mu - 4 leq X) = .36$$
– RHowe
Aug 10 at 0:15
@RHowe Let us hope you believe the correct interpretation is not what you wrote but $$P(X<mu-4)=0.36$$
– Did
Aug 10 at 7:21
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Firstly, I know you don't use $P(X=n)$ in normal distribution questions.
But I have a question where I'm kind of baffled on how to write the probability.
A scientist noted that 36% of temperature measurements were 4°C lower than the average.
I want to say I'd write $P(X<μ-4) = 0.36$ But it just doesn't make sense to me. I would instinctively write $P(X=μ-4) = 0.36$ because I'm looking at values where temperatures are exactly 4°C lower and not at least 4°C lower than the average. So where am I going wrong in understanding this?
probability proof-verification normal-distribution
asked Aug 9 at 23:51
Cheks Nweze
797
Firstly, I know you don't use $P(X=n)$ in normal distribution questions.
But I have a question where I'm kind of baffled on how to write the probability.
A scientist noted that 36% of temperature measurements were 4°C lower than the average.
I want to say I'd write $P(X<μ-4) = 0.36$ But it just doesn't make sense to me. I would instinctively write $P(X=μ-4) = 0.36$ because I'm looking at values where temperatures are exactly 4°C lower and not at least 4°C lower than the average. So where am I going wrong in understanding this?
probability proof-verification normal-distribution
asked Aug 9 at 23:51
Cheks Nweze
797
asked Aug 9 at 23:51
Cheks Nweze
797
asked Aug 9 at 23:51
Cheks Nweze
797
asked Aug 9 at 23:51
Cheks Nweze
797
797
1
The question is poorly stated. If $36%$ were exactly 4°C lower than the average, it certainly wouldn't be a normal distribution, because it wouldn't be continuous. It could be that what is meant is that $36%$ were at least 4°C lower, or perhaps that $36%$ were between $3.5$ and $4.5$ degrees lower.
– Robert Israel
Aug 10 at 0:05
I believe the correct interpretation is $$ Pr(mu - 4 leq X) = .36$$
– RHowe
Aug 10 at 0:15
@RHowe Let us hope you believe the correct interpretation is not what you wrote but $$P(X<mu-4)=0.36$$
– Did
Aug 10 at 7:21
add a comment |Â
1
The question is poorly stated. If $36%$ were exactly 4°C lower than the average, it certainly wouldn't be a normal distribution, because it wouldn't be continuous. It could be that what is meant is that $36%$ were at least 4°C lower, or perhaps that $36%$ were between $3.5$ and $4.5$ degrees lower.
– Robert Israel
Aug 10 at 0:05
I believe the correct interpretation is $$ Pr(mu - 4 leq X) = .36$$
– RHowe
Aug 10 at 0:15
@RHowe Let us hope you believe the correct interpretation is not what you wrote but $$P(X<mu-4)=0.36$$
– Did
Aug 10 at 7:21
1
1
The question is poorly stated. If $36%$ were exactly 4°C lower than the average, it certainly wouldn't be a normal distribution, because it wouldn't be continuous. It could be that what is meant is that $36%$ were at least 4°C lower, or perhaps that $36%$ were between $3.5$ and $4.5$ degrees lower.
– Robert Israel
Aug 10 at 0:05
The question is poorly stated. If $36%$ were exactly 4°C lower than the average, it certainly wouldn't be a normal distribution, because it wouldn't be continuous. It could be that what is meant is that $36%$ were at least 4°C lower, or perhaps that $36%$ were between $3.5$ and $4.5$ degrees lower.
– Robert Israel
Aug 10 at 0:05
I believe the correct interpretation is $$ Pr(mu - 4 leq X) = .36$$
– RHowe
Aug 10 at 0:15
I believe the correct interpretation is $$ Pr(mu - 4 leq X) = .36$$
– RHowe
Aug 10 at 0:15
@RHowe Let us hope you believe the correct interpretation is not what you wrote but $$P(X<mu-4)=0.36$$
– Did
Aug 10 at 7:21
@RHowe Let us hope you believe the correct interpretation is not what you wrote but $$P(X<mu-4)=0.36$$
– Did
Aug 10 at 7:21
add a comment |Â
1 Answer
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You are correct to question this. I think the fault is in the statement
A scientist noted that 36% of temperature measurements were 4°C lower than the average.
Imagine taking lots of temperature measurements and finding that $36%$ were exactly 4°C. It wouldn’t happen, since temperature is a continuous variable.
Perhaps it should state:
A scientist noted that 36% of temperature measurements were 4°C lower than the average, to the nearest whole degree.
Or
A scientist noted that 36% of temperature measurements were at least 4°C lower than the average.
In either of these cases I’m sure you can figure out what probability to use.
answered Aug 10 at 0:11
Malkin
1,482523
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
You are correct to question this. I think the fault is in the statement
A scientist noted that 36% of temperature measurements were 4°C lower than the average.
Imagine taking lots of temperature measurements and finding that $36%$ were exactly 4°C. It wouldn’t happen, since temperature is a continuous variable.
Perhaps it should state:
A scientist noted that 36% of temperature measurements were 4°C lower than the average, to the nearest whole degree.
Or
A scientist noted that 36% of temperature measurements were at least 4°C lower than the average.
In either of these cases I’m sure you can figure out what probability to use.
answered Aug 10 at 0:11
Malkin
1,482523
add a comment |Â
up vote
1
down vote
accepted
You are correct to question this. I think the fault is in the statement
A scientist noted that 36% of temperature measurements were 4°C lower than the average.
Imagine taking lots of temperature measurements and finding that $36%$ were exactly 4°C. It wouldn’t happen, since temperature is a continuous variable.
Perhaps it should state:
A scientist noted that 36% of temperature measurements were 4°C lower than the average, to the nearest whole degree.
Or
A scientist noted that 36% of temperature measurements were at least 4°C lower than the average.
In either of these cases I’m sure you can figure out what probability to use.
answered Aug 10 at 0:11
Malkin
1,482523
add a comment |Â
up vote
1
down vote
accepted
up vote
1
down vote
accepted
You are correct to question this. I think the fault is in the statement
A scientist noted that 36% of temperature measurements were 4°C lower than the average.
Imagine taking lots of temperature measurements and finding that $36%$ were exactly 4°C. It wouldn’t happen, since temperature is a continuous variable.
Perhaps it should state:
A scientist noted that 36% of temperature measurements were 4°C lower than the average, to the nearest whole degree.
Or
A scientist noted that 36% of temperature measurements were at least 4°C lower than the average.
In either of these cases I’m sure you can figure out what probability to use.
answered Aug 10 at 0:11
Malkin
1,482523
You are correct to question this. I think the fault is in the statement
A scientist noted that 36% of temperature measurements were 4°C lower than the average.
Imagine taking lots of temperature measurements and finding that $36%$ were exactly 4°C. It wouldn’t happen, since temperature is a continuous variable.
Perhaps it should state:
A scientist noted that 36% of temperature measurements were 4°C lower than the average, to the nearest whole degree.
Or
A scientist noted that 36% of temperature measurements were at least 4°C lower than the average.
In either of these cases I’m sure you can figure out what probability to use.
answered Aug 10 at 0:11
Malkin
1,482523
answered Aug 10 at 0:11
Malkin
1,482523
answered Aug 10 at 0:11
Malkin
1,482523
answered Aug 10 at 0:11
Malkin
1,482523
1,482523
add a comment |Â
add a comment |Â
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1
The question is poorly stated. If $36%$ were exactly 4°C lower than the average, it certainly wouldn't be a normal distribution, because it wouldn't be continuous. It could be that what is meant is that $36%$ were at least 4°C lower, or perhaps that $36%$ were between $3.5$ and $4.5$ degrees lower.
– Robert Israel
Aug 10 at 0:05
I believe the correct interpretation is $$ Pr(mu - 4 leq X) = .36$$
– RHowe
Aug 10 at 0:15
@RHowe Let us hope you believe the correct interpretation is not what you wrote but $$P(X<mu-4)=0.36$$
– Did
Aug 10 at 7:21