Answer:
a) Mean = 0.75
b) Standard error = 0.051
c) Yes
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 50
Sample proportion , p = 0.15
a) Mean
b) Standard error
c) Application of central limit theorem
Since the sample size is larger than 30, we cam apply central limit theorem for normal approximation.
Answer: (0, 0) & (3, √3)
<u>Step-by-step explanation:</u>
Since we need a distance of 2, I graphed y = √x and then drew a circle at center (2, 0) and radius of 2 to see where they intersect.
The coordinates of intersection can be determined by solving a system of equations.
Equation 1: y = √x
Equation 2: (x - 2)² + y² = 2²
I will use the Substitution method with Equation 2 to solve for x:
(x - 2)² + (√x)² = 2² substituted y with √x
x² - 4x + 4 + x = 4 expanded binomial
x² - 3x + 4 = 4 added like terms
x² - 3x = 0 subtracted 4 from both sides
x(x - 3) = 0 factored
x = 0 x - 3 = 0 applied Zero Product Property
x = 3
Next, solve for y using Equation 1:
x = 0: y = √0 = 0
x = 3: y = √3
Coordinates of intersection are: (0, 0) & (3, √3)
