Expert: Scott A Wilson - 6/20/2009

Question
QUESTION: A certain tribe is distinguished by the fact that 45% of the males have 6 toes on their right foot. 2 explorers discover a group of 200 males from the tribe. Find the probability that the number who have 6 toes on their right foot is a)90, b)less than 85, c)between 82 & 31 inclusive, d)more than 97. Thanks you very much

ANSWER: Again, the binomial is being approximated with the normal.
The number n is 200.  The probability p is 0.45.
The average is 200 * 0.45 = 90.
The standard deviation is √(200*0.45*0.55).

a) To be greater than 90 in the binomial is to be greater the 89.5 in the normal.  Determine how far each number is from the average and divide by the standard deviation.  This will give the value to look up on the normal table.

b) Less than 85 means 85 is not included, so find the number below 84.5 in the normal.

c) Between 82 and 31 inclusive means to include 82 and 31.
Determine the chance of being between 30.5 and 82.5 in the normal.

d) The chance of being more than 97 means the normal chance of being more than 97.5.


---------- FOLLOW-UP ----------

QUESTION: I have difficulty in determining which is n and which is p for some of the questions like this. Can you it explain briefly? Why n cannot be equal to 6? Sometimes i confuse by putting n= 20 or other way around n=6. Cheers

Answer
I have all four problems answered and will be sending them shortly.
Unless of course something else comes up, but I think I'm free for at least an hour.

Your understanding of American English is great since I can easily understand your questions.  However, there are few comments that I have that could make it even better.

For QUESTION: Thanks for your help. Based on your explaination, i found out some wrong working. Just want to told you & in case others people didnt notice it too. Your var is wrongly calculate. Part i) & ii) didnt said it is inclusive so part i) should be p(x>60) -> p(x>60.5) & part ii) p(x<45) -> p(x<44.5) & for part b, i have shortcut, (.75)^n>.9. Apply log on both sides, n log .75< log .1. Lastly, i really much appreciate your help.

1: "didnt" should have an apostrophe in it as "didn't", since it is short for "did not".

2: "why put = sign" would sound better as "why do you put an equals sign".

3: "explaination" is really "explantation".

4: "i" is usually "I".

5: "didnt said"  should be "didn't say"

In, "QUESTION: Thanks you very much for spending your precious time in helping me. Why the expected value not 200*6 instead of 200/6 ? Can you explain, i dont get it? Part c & d, didnt state it is inclusive so i think part c) should be p(x>38.5) & part d) p(x<27.5). Much appreciated"

1. "Why the" should be "Why was the".

2. "explain, i" should be "explain - I" or "explain ... I"

3. "Part c & d, didnt state it is inclusive" should be
"Parts c & d didn't state it was inclusive, "; change "Part" to "Parts"; added  ' in "didn't"; change 'is' to 'was'.

QUESTION: I have difficulty in determining which is n and which is p for some of the questions like this. Can you it explain briefly? Why n cannot be equal to 6? Sometimes i confuse by putting n= 20 or other way around n=6. Cheers

1. The word "cannot" can also be "can't".

2. The sentence "Sometimes i confuse by putting n= 20 or other way around n=6." could be better as "Sometimes I get confused as to whether to use n=20 or n=6."


Now that that was said, lets get on with the question.

The variable n is often used fro the number since number starts with n.  It is used for the same size.  In this case, it is the number of males to be tested.

The variable p is often used for probability since probability start with p.

The 6 is the number of toes that could be on each person in question.  Note that the other number of toes is 5.