He really enjoys swinging nightclubs
Answer:
The null and alternative hypothesis for this test are
Step-by-step explanation:
If we perform a hypothesis test, we can reject or not reject the null hypothesis.
To conclude that the tires have a decreased stopping distance (μ<215), we should state the null hypothesis 
and then go on with the analysis to reject it (or not).
If the null hypothesis is rejected, the claim of the manufacturer is rigth.
The alternative hypothesis would be 
, that would turn rigth if the null hypothesis is rejected.
Answer:
C
Step-by-step explanation:
Use formula
where
I = interest
P = rpincipal
r = rate (as decimal)
t = time (in years)
In your case,
P = $800
r = 0.04 (4%)
t = 5,
so
Answer:
the expected value of Xn , E(Xn) = 0 and the variance σ²(Xn) = n*(1-2n)
Step-by-step explanation:
If X1= number of tails when n fair coins are flipped , then X1 follows a binomial distribution with E(X1) = n*p , p=0,5 and the number of heads obtained is X2=n-X1
therefore
Xn =X1-X2 = X1- (n-X1) = 2X1-n
thus
E(Xn) =∑ (2*X1-n) p(X1) = 2*∑[X1 p(X1)] -n∑p(X1) = 2*E(X1)-n = 2*n*p--n= 2*n*1/2 -n = n-n =0
the variance will be
σ²(Xn) = ∑ [Xn - E(Xn)]² p(Xn) = ∑ [(2X1-n) - 0 ]² p(X1) = ∑ (4*X1²-4*X1*n+n²) p(X1) = = 4*∑ X1²p(X1) - 4n ∑X1 p(X1) - n²∑p(X1) = 2*E(X1²) -4n*E(X1)- n²
since
σ²(X1) = n*p*(1-p) = n*0,5*0,5=n/4
and
σ²(X1) = E(X1²) - [E(X1)]²
n/4 = E(X1²) - (n/2)²
E(X1²) = n(n+1)/4
therefore
σ²(Xn) = 4*E(X1²) -4n*E(X1)- n² = 4*n(n+1)/4 - 4*n*n/2 - n² = n(n+1) - 2n² - n²
= n - 2n² = n(1-2n)
σ²(Xn) = n(1-2n)
