Question

The heights of a certain group of adult parrots were found to be normally distributed. The mean height is 36 cm with a standard deviation of 7 cm. In a group of 1200 of these birds, how many would be more than 29 cm tall?

Answer 1

1010

Explanation:

Let `X` be the height of the birds. `X` is distributed normally so we write it: `X ~ N(36, 7^2)`. The expected number of birds more than 29cm tall will be 1200 multiplied by P(Bird is taller than29cm).
`P(X > 29)`
First, standardise the normal by making it a `z` value.
`=P(Z > \frac{29-36}{7}) = P(Z > -1)`
And in the normal distribution: `P(Z > -z) = P(Z < z)`
So `P(Z > -1) = P(Z < 1)`.
Using stat tables you can find that `P(Z < 1) = 0.8413`.
So the expected no. birds taller than 29cm is `0.8413 * 1200 = 1010` rounded to the nearest no. birds.