Answer:
b) 0.2961
c) 0.2251
d) Mean = 11.25, Standard deviation = 1.667
Step-by-step explanation:
We are given the following information:
We treat trucks undergoing a brake inspection passin as a success.
P( trucks undergoing a brake inspection passes the test) = 75% = 0.75
a) Conditions for binomial probability distribution
- There are n independent trial.
- Each trial have a success probability p
- The probability of success is same for all trials.
Then the number of trucks undergoing a brake inspection follows a binomial distribution, where
where n is the total number of observations, x is the number of success, p is the probability of success.
Now, we are given n = 15
b) P(proportion of groups will between 8 and 10 trucks pass the inspection)
We have to evaluate:
c) P( exactly 3 trucks fail the inspection)
p = 0.25
d) Mean and standard deviation

4. SOLVE FOR X:
Using the Alternate Interior Angles Theorem, we know that the 67 degree angle is congruent with the (12x - 5) degree angle. With this information, all I have to do is set the two equal to each other and solve for x.
67 = 12x - 5
67 + 5 = 12x - 5 + 5
72/12 = 12x/12
6 = x
x = 6
SOLVE FOR Y:
Using the Vertical Angles theorem, we know that angle y must be congruent to the 67 degree angle.
y = 67 degrees.
5. SOLVE FOR Y:
Alternate exterior angles: 6(x - 12) = 120
6x - 72 + 72 = 120 + 72
6x/6 = 192/6
x = 32
SOLVE FOR Y:
6((32) - 12) + y = 180
192 - 72 + y = 180
120 + y - 120 = 180 - 120
y = 60
This is a volume question. 8x8x8, 512 cubic inches of water.