Step-by-step explanation:
Given points are (-2,5) and (3,-17)
to find midpoint, use this formula
( x1+x2/2 , y1+y2/2)
where points are a(x1,y1) and b(x2,y2)
coming to the question,
midpoint is :
[ (-2-3)/2 , (5-17)/2 ]
[ -5/2 , -12/2 ]
[ -2.5 , -6 ]
OPTION IS CORRECT
Answer:
Step-by-step explanation:
Hello!
Given the probabilities:
P(A₁)= 0.35
P(A₂)= 0.50
P(A₁∩A₂)= 0
P(BIA₁)= 0.20
P(BIA₂)= 0.05
a)
Two events are mutually exclusive when the occurrence of one of them prevents the occurrence of the other in one repetition of the trial, this means that both events cannot occur at the same time and therefore they'll intersection is void (and its probability zero)
Considering that P(A₁∩A₂)= 0, we can assume that both events are mutually exclusive.
b)
Considering that you can clear the intersection from the formula
and apply it for the given events:
c)
The probability of "B" is marginal, to calculate it you have to add all intersections where it occurs:
P(B)= (A₁∩B) + P(A₂∩B)= 0.07 + 0.025= 0.095
d)
The Bayes' theorem states that:
Then:
I hope it helps!
Answer:
Explained below.
Step-by-step explanation:
(1)
The hypothesis can be defined as follows:
<em>H</em>₀: The Speedy Oil Change will change the oil in customers’ cars in more than 30 minutes on average, i.e. <em>μ</em> > 30.
<em>H</em>ₐ: The Speedy Oil Change will change the oil in customers’ cars in less than 30 minutes on average, i.e. <em>μ</em> ≤ 30.
(2)
Use Excel to compute the sample mean and standard deviation as follows:
Compute the test statistic as follows:
The degrees of freedom is:
df = n - 1
= 36 - 1
= 35
Compute the p-value as follows:
(3)
The <em>p</em>-value = 0.0006 is very small.
The null hypothesis will be rejected at any of the commonly used significance level.
(4)
There is sufficient evidence to support the claim that the Speedy Oil Change will change the oil in customers’ cars in less than 30 minutes on average.
