# 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?

Jun 6, 2017

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).
$P \left(X > 29\right)$
First, standardise the normal by making it a $z$ value.
$= P \left(Z > \setminus \frac{29 - 36}{7}\right) = P \left(Z > - 1\right)$
And in the normal distribution: $P \left(Z > - z\right) = P \left(Z < z\right)$
So $P \left(Z > - 1\right) = P \left(Z < 1\right)$.
Using stat tables you can find that $P \left(Z < 1\right) = 0.8413$.
So the expected no. birds taller than 29cm is $0.8413 \cdot 1200 = 1010$ rounded to the nearest no. birds.