Assume a binomial distribution. Then the mean of the distribution is , where
is the number of people taken in a sample and
is the probability of the mutation occurring in any given person, and the standard deviation is
. Then in this case, the standard deviation is
.
Answer:
(a) Five
(b) Thirteenth
Step-by-step explanation:
We have the mean is 12.6 and
that 11 occurs 4 times, 12 occurs 7 times, 13 occurs 9 times, and 14 occurs f times.
How many children are there in all (that is the sum of the frequencies).
4+7+9+f
20+f
Alright so the mean could be found by doing:
But we are given this is also equal to: 12.6.
So we have
I'm going to simplify what I can on top.
I'm going to write 12.6 as because I want to cross multiply:
Distribute:
Subtract 12.6f on both sides:
Subtract 245 on both sides:
Divide both sides by 1.4:
There are five 14 years old.
(b) I would say 13 is good age to represent this bunch.
The means was 12.6 which when rounded is 13.
The mode is 13 because it is the most occurring
The median is also 13. Why? If you list out the data 13 will be the middle number. Or you could say there are 25 kids and if I divide it by 2, I get 12.5. This means you only need to count to the 13th kid with the ages in order to tell with the median is.
There are 4 eleven yr olds.
There are 7 twelve yr olds. That is 11 kids so far.
So the median has to be included in the 9 thirteenth yr olds.