Answer:
Step-by-step 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!
