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




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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














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




share|cite|improve this question
















  • 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












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




share|cite|improve this question












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





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asked Aug 9 at 23:51









Cheks Nweze

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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












  • 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










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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.






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    up vote
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    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.






    share|cite|improve this answer
























      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.






      share|cite|improve this answer






















        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.






        share|cite|improve this answer












        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.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Aug 10 at 0:11









        Malkin

        1,482523




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