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?

1 Answer
Jun 6, 2017

1010

Explanation:

Let X be the height of the birds. X is distributed normally so we write it: X~N(36,72). 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>29367)=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 0.84131200=1010 rounded to the nearest no. birds.