Question

Please can any one help?
According to genetic theory, plants of a particular species have a 25% chance of being red-flowering, independently of other plants. Find the normal approximation to the chance that among 10,000 plants of this species, more than 2400 are red-flowering.
Approach:You want P(X>2400) when X follows a binomial distribution with p=0.25 and N=10000.
You need a normal approximation Y to X - that is, you should match the mean and variance of Y to those of X. Then you can approximate your answer using P(Y>2400)?

Answer 1

Find P(X>2400), using P(Y>2400) as a normal approximation.

First find the mean for the population of 10000. Since p=0.25, the expected amount (mean) of red flowering plants is:

\[\Large E(x) = np = 0.25*10000 = 2500\]
Standard deviation for the normal approximation is given by \[\Large SD = \sqrt{ np (1-p)} = \sqrt{ 2500 (1-0.25)} = 43.301\]

Now we can find the z-score so we can find P(Y>2400). z score is given by \[\Large z = \frac{ X - mean }{ SD }\]
\[\Large z = \frac{ 2400 - 2500 }{ 43.301 } = -2.31\]

Now you just have to use a z chart to solve: http://www.mathsisfun.com/data/standard-normal-distribution-table.html

You need P(z>-2.31)...ie the area to the right of -2.31

Answer 2

Or: http://www.wolframalpha.com/input/?i=P%28z%3E-2.31%29

Answer 3

If you're confused, this site has step by step directions to a similar problem: http://www.statisticshowto.com/articles/using-the-normal-approximation-to-solve-a-binomial-problem/

I didn't use the continuity correction factor, but it makes ~no difference in this question anyway.

Answer 4

Answer is 0.9896 - (if somebody has problem with "SticiGui")

Answer 5

is the answer is 98.96% or 0.9896

Answer 6

One of them is a percentage probability, the other is a decimal probability...

Answer 7

the lower limit -2.31 and upper limit 5 area under the normal curve =98.96%=0.9896 is slot answer

Answer 8

thanks agent0smith

Answer 9

0.9896 - decimal is right (without %)

Answer 10

Thanks Oles if You enter in percent 98.96 You get it wrong so its correct to enter always in slot answer 0.9896!

Answer 11

@Oles 98.96% is also correct. Just depends on what answer the test wants, a percentage or decimal. They're equivalent.

Answer 12

in our case for this type it wants decimal agent0smith thanks both are correct!

Answer 13

Hi!
I will put to my attantion that answer is accept both formats: percentage and decimal.
In any case its extra experiance for me ;-)
Thanks