Question

he weight of male babies less than months old in the United States is normally distributed with mean pounds and standard deviation pounds. (a) Find the nd percentile of the baby weights. (b) Find the th percentile of the baby weights. (c) Find the first quartile of the baby weights. Use the TI-84 Plus calculator and round the answers to at least two decimal places.

Answer 1

Explanation:

Hello!

The variable of interest is

X: Weight of a male baby (pounds)

X~N(μ;σ²)

μ= 11.5 pounds

σ= 2.7 pounds

a) Find the 81st percentile of the baby weights.

This percentile is the value that separates the bottom 81% of the distribution from the top 19%

P(X≤x₁)= 0.81

For this you have to use the standard normal distribution. First you have to look the 81st percentile under the Z distribution and then "translate" it to a value of the variable X using the formula Z= (X- μ)/σ

P(Z≤z₁)= 0.81

z₁= 0.878

z₁= (x₁- μ)/σ

z₁*σ= x₁- μ

(z₁*σ) + μ= x₁

x₁= (z₁*σ) + μ

x₁= (2.7*0.878)+11.5

x₁= 13.8706 pounds

b) Find the 10th percentile of the baby weights.

P(X≤x₂)= 0.10

P(Z≤z₂)= 0.10

z₂= -1.282

z₂= (x₂- μ)/σ

z₂*σ= x₂- μ

(z₂*σ) + μ= x₂

x₂= (z₂*σ) + μ

x₂= (2.7*-1.282)+11.5

x₂= 8.0386 pounds

c) Find the first quartile of the baby weights.

P(X≤x₃)= 0.25

P(Z≤z₃)= 0.25

z₃= -0.674

z₃= (x₃- μ)/σ

z₃*σ= x₃- μ

(z₃*σ) + μ= x₃

x₃= (z₃*σ) + μ

x₃= (2.7*-0.674)+11.5

x₃= 9.6802 pounds

I hope this helps!