Question

A pediatrician treats many children in her practice. Among the children who are currently 4 years old, the average height is 39.5 inches, with an SD of 2.1 inches. A histogram of the heights approximately follows the normal curve.

(a) About what percentage of the 4 year olds are between 35 and 40 inches tall?

(b) Approximately 95% of the 4 year olds are between ________ and _________ inches tall.

(c) Find the 80th percentile of the heights. _________________ inches

Answer 1

This is a normal distribution question with


a)
P(35.0 < x < 40.0)=?

This implies that

b)
95% of the value will be in between p=0.025 & p=0.975

Given in the question
P(X < x) = 0.025
This implies that
P(Z < -1.9599639845400545) = 0.025
With the help of formula for z, we can say that

&

P(X < x) = 0.975
This implies that
P(Z < 1.959963984540054) = 0.975
With the help of formula for z, we can say that

95% of the value will be in between 35.3841 & 43.6159 inches tall

c)
Given in the question
P(X < x) = 0.8
This implies that
P(Z < 0.8416212335729143) = 0.8
With the help of formula for z, we can say that

PS: you have to refer z score table to find the final probabilities.
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