Suppose the heights of a population of $3,000$ adult penguins are approximately normally distributed with a...












1














I would like to check myself if following my answer is correct: let us consider following problem:



Suppose the heights of a population of $3,000$ adult penguins are approximately normally distributed with a mean of $65$ centimeters and a standard deviation of $5$ centimeters.



(a) Approximately how many of the adult penguins are between $65$ centimeters and $75$ centimeters
tall?



(b) If an adult penguin is chosen at random from the population, approximately what is the probability that the penguin’s height will be less than $60$ centimeters? Give your answer to the nearest 0.05.



so as i know approximately $68$ or $2/3$ fall in the interval of $[mu-sigma,mu+sigma]$,approximately $96$ fall between $[mu-2*sigma,mu+2*sigma]$



and approximately $99$% fall between



$[mu-3*sigma,mu+3*sigma]$



now we are asked between $75$ and $65$,which is equal



$[mu-2*sigma,mu+2*sigma]$



this range,but in this case it is second half range,in this range it would be half of or $48$%,which means that number of penguins would be $3000*0.48=1440$ penguins would be,am i correct?



on (b), less then $60$ means that below $65-5$ or below $[mu-sigma]$ or $16$ percent would be fall in this interval,am i correct?please help me






normal-distribution







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  • I think everything looks good.
    – angryavian
    Aug 2 '13 at 5:47










  • only one thing which i did not understand is that,instead of $0.16$,there is $0.15$ in answers
    – giorgi
    Aug 2 '13 at 5:49












  • maybe because it is less then $60$,itself $60$ or $1$ % is not counted?
    – giorgi
    Aug 2 '13 at 6:02












  • For the first, $41432$ is closer to what is given by the tables. The $68%$ you used is somewhat imprecise. For the second, they rounded to the nearest $.05$. That is what the question asked for. Your $16%$ is closer to the truth.
    – André Nicolas
    Aug 2 '13 at 6:03












  • No, regardless of whether the question is asking for $<60$ or $le 60$, the answer is the same. However, I see the reason: they ask you to round to the nearest 0.05
    – angryavian
    Aug 2 '13 at 6:03
















1














I would like to check myself if following my answer is correct: let us consider following problem:



Suppose the heights of a population of $3,000$ adult penguins are approximately normally distributed with a mean of $65$ centimeters and a standard deviation of $5$ centimeters.



(a) Approximately how many of the adult penguins are between $65$ centimeters and $75$ centimeters
tall?



(b) If an adult penguin is chosen at random from the population, approximately what is the probability that the penguin’s height will be less than $60$ centimeters? Give your answer to the nearest 0.05.



so as i know approximately $68$ or $2/3$ fall in the interval of $[mu-sigma,mu+sigma]$,approximately $96$ fall between $[mu-2*sigma,mu+2*sigma]$



and approximately $99$% fall between



$[mu-3*sigma,mu+3*sigma]$



now we are asked between $75$ and $65$,which is equal



$[mu-2*sigma,mu+2*sigma]$



this range,but in this case it is second half range,in this range it would be half of or $48$%,which means that number of penguins would be $3000*0.48=1440$ penguins would be,am i correct?



on (b), less then $60$ means that below $65-5$ or below $[mu-sigma]$ or $16$ percent would be fall in this interval,am i correct?please help me






normal-distribution







share|cite|improve this question
























  • I think everything looks good.
    – angryavian
    Aug 2 '13 at 5:47










  • only one thing which i did not understand is that,instead of $0.16$,there is $0.15$ in answers
    – giorgi
    Aug 2 '13 at 5:49












  • maybe because it is less then $60$,itself $60$ or $1$ % is not counted?
    – giorgi
    Aug 2 '13 at 6:02












  • For the first, $41432$ is closer to what is given by the tables. The $68%$ you used is somewhat imprecise. For the second, they rounded to the nearest $.05$. That is what the question asked for. Your $16%$ is closer to the truth.
    – André Nicolas
    Aug 2 '13 at 6:03












  • No, regardless of whether the question is asking for $<60$ or $le 60$, the answer is the same. However, I see the reason: they ask you to round to the nearest 0.05
    – angryavian
    Aug 2 '13 at 6:03














1












1








1







I would like to check myself if following my answer is correct: let us consider following problem:



Suppose the heights of a population of $3,000$ adult penguins are approximately normally distributed with a mean of $65$ centimeters and a standard deviation of $5$ centimeters.



(a) Approximately how many of the adult penguins are between $65$ centimeters and $75$ centimeters
tall?



(b) If an adult penguin is chosen at random from the population, approximately what is the probability that the penguin’s height will be less than $60$ centimeters? Give your answer to the nearest 0.05.



so as i know approximately $68$ or $2/3$ fall in the interval of $[mu-sigma,mu+sigma]$,approximately $96$ fall between $[mu-2*sigma,mu+2*sigma]$



and approximately $99$% fall between



$[mu-3*sigma,mu+3*sigma]$



now we are asked between $75$ and $65$,which is equal



$[mu-2*sigma,mu+2*sigma]$



this range,but in this case it is second half range,in this range it would be half of or $48$%,which means that number of penguins would be $3000*0.48=1440$ penguins would be,am i correct?



on (b), less then $60$ means that below $65-5$ or below $[mu-sigma]$ or $16$ percent would be fall in this interval,am i correct?please help me






normal-distribution







share|cite|improve this question















I would like to check myself if following my answer is correct: let us consider following problem:



Suppose the heights of a population of $3,000$ adult penguins are approximately normally distributed with a mean of $65$ centimeters and a standard deviation of $5$ centimeters.



(a) Approximately how many of the adult penguins are between $65$ centimeters and $75$ centimeters
tall?



(b) If an adult penguin is chosen at random from the population, approximately what is the probability that the penguin’s height will be less than $60$ centimeters? Give your answer to the nearest 0.05.



so as i know approximately $68$ or $2/3$ fall in the interval of $[mu-sigma,mu+sigma]$,approximately $96$ fall between $[mu-2*sigma,mu+2*sigma]$



and approximately $99$% fall between



$[mu-3*sigma,mu+3*sigma]$



now we are asked between $75$ and $65$,which is equal



$[mu-2*sigma,mu+2*sigma]$



this range,but in this case it is second half range,in this range it would be half of or $48$%,which means that number of penguins would be $3000*0.48=1440$ penguins would be,am i correct?



on (b), less then $60$ means that below $65-5$ or below $[mu-sigma]$ or $16$ percent would be fall in this interval,am i correct?please help me






normal-distribution




normal-distribution






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share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Feb 26 '18 at 4:53









Palautot Ka

9201518




9201518










asked Aug 2 '13 at 5:40









giorgi

1371213




1371213












  • I think everything looks good.
    – angryavian
    Aug 2 '13 at 5:47










  • only one thing which i did not understand is that,instead of $0.16$,there is $0.15$ in answers
    – giorgi
    Aug 2 '13 at 5:49












  • maybe because it is less then $60$,itself $60$ or $1$ % is not counted?
    – giorgi
    Aug 2 '13 at 6:02












  • For the first, $41432$ is closer to what is given by the tables. The $68%$ you used is somewhat imprecise. For the second, they rounded to the nearest $.05$. That is what the question asked for. Your $16%$ is closer to the truth.
    – André Nicolas
    Aug 2 '13 at 6:03












  • No, regardless of whether the question is asking for $<60$ or $le 60$, the answer is the same. However, I see the reason: they ask you to round to the nearest 0.05
    – angryavian
    Aug 2 '13 at 6:03


















  • I think everything looks good.
    – angryavian
    Aug 2 '13 at 5:47










  • only one thing which i did not understand is that,instead of $0.16$,there is $0.15$ in answers
    – giorgi
    Aug 2 '13 at 5:49












  • maybe because it is less then $60$,itself $60$ or $1$ % is not counted?
    – giorgi
    Aug 2 '13 at 6:02












  • For the first, $41432$ is closer to what is given by the tables. The $68%$ you used is somewhat imprecise. For the second, they rounded to the nearest $.05$. That is what the question asked for. Your $16%$ is closer to the truth.
    – André Nicolas
    Aug 2 '13 at 6:03












  • No, regardless of whether the question is asking for $<60$ or $le 60$, the answer is the same. However, I see the reason: they ask you to round to the nearest 0.05
    – angryavian
    Aug 2 '13 at 6:03
















I think everything looks good.
– angryavian
Aug 2 '13 at 5:47




I think everything looks good.
– angryavian
Aug 2 '13 at 5:47












only one thing which i did not understand is that,instead of $0.16$,there is $0.15$ in answers
– giorgi
Aug 2 '13 at 5:49






only one thing which i did not understand is that,instead of $0.16$,there is $0.15$ in answers
– giorgi
Aug 2 '13 at 5:49














maybe because it is less then $60$,itself $60$ or $1$ % is not counted?
– giorgi
Aug 2 '13 at 6:02






maybe because it is less then $60$,itself $60$ or $1$ % is not counted?
– giorgi
Aug 2 '13 at 6:02














For the first, $41432$ is closer to what is given by the tables. The $68%$ you used is somewhat imprecise. For the second, they rounded to the nearest $.05$. That is what the question asked for. Your $16%$ is closer to the truth.
– André Nicolas
Aug 2 '13 at 6:03






For the first, $41432$ is closer to what is given by the tables. The $68%$ you used is somewhat imprecise. For the second, they rounded to the nearest $.05$. That is what the question asked for. Your $16%$ is closer to the truth.
– André Nicolas
Aug 2 '13 at 6:03














No, regardless of whether the question is asking for $<60$ or $le 60$, the answer is the same. However, I see the reason: they ask you to round to the nearest 0.05
– angryavian
Aug 2 '13 at 6:03




No, regardless of whether the question is asking for $<60$ or $le 60$, the answer is the same. However, I see the reason: they ask you to round to the nearest 0.05
– angryavian
Aug 2 '13 at 6:03










1 Answer
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oldest

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For rounding 16% to the nearest 0.05 percent you should do the following calculations:
First divide 16% by 0.05: (16%/0.05) = 3.2. Then, round 3.2 to the nearest point = 3.
Now, you should multiply 3 to 0.05 = 0.15.



Good Luck






share|cite|improve this answer





















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    1 Answer
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    1 Answer
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    For rounding 16% to the nearest 0.05 percent you should do the following calculations:
    First divide 16% by 0.05: (16%/0.05) = 3.2. Then, round 3.2 to the nearest point = 3.
    Now, you should multiply 3 to 0.05 = 0.15.



    Good Luck






    share|cite|improve this answer


























      0














      For rounding 16% to the nearest 0.05 percent you should do the following calculations:
      First divide 16% by 0.05: (16%/0.05) = 3.2. Then, round 3.2 to the nearest point = 3.
      Now, you should multiply 3 to 0.05 = 0.15.



      Good Luck






      share|cite|improve this answer
























        0












        0








        0






        For rounding 16% to the nearest 0.05 percent you should do the following calculations:
        First divide 16% by 0.05: (16%/0.05) = 3.2. Then, round 3.2 to the nearest point = 3.
        Now, you should multiply 3 to 0.05 = 0.15.



        Good Luck






        share|cite|improve this answer












        For rounding 16% to the nearest 0.05 percent you should do the following calculations:
        First divide 16% by 0.05: (16%/0.05) = 3.2. Then, round 3.2 to the nearest point = 3.
        Now, you should multiply 3 to 0.05 = 0.15.



        Good Luck







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Nov 2 '15 at 12:00









        user286183

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