Question

It is believed that on average 40 % of all children have some kind of nut allergy. A kindergarten has registered 260 incoming children. With 95% certainty, what is the lowest number of children that will have any kind of nut allergy among the 260 incoming children. (Hint: 95% certainty is equivalent to 2 standard deviations above and below the mean).

Answer 1

Answer:

Given that:

It is believed that on average 40 % of all children have some kind of nut allergy. A kindergarten has registered 260 incoming children.

With 95% certainty, what is the lowest number of children that will have any kind of nut allergy among the 260 incoming children.

We have 260 incoming children on average 40% have nut allergy.

So mean number of children having null allergy in the incoming ones

= 260 *0.40

= 104

Variance = 260^2 * 0.40 - (104)^2

= 67600 * 0.40 - 10816

= 27040 - 10816

= 16,224

Standard deviation =

=

=

Now, 95% certaintly equivalent is 2 S.D above and below in the meanSo the lowest number of children having allergy

=

=

=

=

=

The required number of children is 89.