The heights of a certain group of adult parrots were

Elsa Barron

Elsa Barron

Answered question

2022-01-27

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 & Explanation

basgrwthej

basgrwthej

Beginner2022-01-28Added 13 answers

Explanation:
Let X be the height of the birds. X is distributed normally so we write it:
XN(36,72). The expected number of birds more than 29cm tall will be 1200 multiplied by P(Bird is taller than 29cm).
P(X>29)
First, standardise the normal by making it a z value.
=P(Z>29367)=P(Z1)
And in the normal distribution: P(Z>-z)=P(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.

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