Answer:
The mean of the sampling distribution of the sample proportions is 0.82 and the standard deviation is 0.0256.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean 
and standard deviation 
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation 
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For proportions, the mean is 
and the standard deviation is 
In this problem, we have that:
.
So
The mean of the sampling distribution of the sample proportions is 0.82 and the standard deviation is 0.0256.
Answer:
C(5,-4), D(-4,-4)
Have a great day :)
Step-by-step explanation:
Answer:
Jennifer - 1st
Susan - 2nd
Emily - 3rd
Janice - 4th
Maria - 5th
Step-by-step explanation:
Susan is 2nd.
Places 1, 3, 4, and 5 are left.
Janice and Jennifer both start with J. None of the other swimmers start with the same first letter. One is 1st and one is 4th.
Since Maria finished immediately after Janice, and Janice must be 1st or 4th, Janice can't be first since 2nd place is already taken. This means that Janice is 4th and Maria is 5th.
Places 1 and 3 are left.
We know Jennifer is 1st or 4th and since 4th is taken, Jennifer is first.
Place 3 is left.
Emily must be 3rd since that is the only spot left.
Answer:
x₁ = -4
x₂ = 3
Step-by-step explanation:
x²+ x + 12 = 0
x = {-1±√((1²)-(4*1*-12))} / (2*1)
x = {-1±√(1+48)} / 2
x = {-1±√49} / 2
x = {-1±7} / 2
x₁ = {-1-7} / 2 = -8/2 = -4
x₂ = {-1+7} / 2 = 6/2 = 3
Check:
x₁
-4² + (-4) - 12 = 0
16 - 4 - 12 = 0
x₂
3² + 3 - 12 = 0
9 + 3 - 12 = 0
