8. Tourists marvel at Niagara Falls from two sightseeing boats, A and B. The boats are 100 feet and
150 feet away from the base of the falls, respectively. Given that Niagara Falls is 167 feet high,
what is the angle of elevation from both boats to the top of the falls?

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!