Suppose that 75% of all trucks undergoing a brake inspection at a certain inspection facility pass the inspection. Consider groups of 15 trucks and let X be the number of trucks in a group that have passed the nspection Part a: Verify that this is a binomial distribution Part b: For what proportion of groups will between 8 and 10 trucks (inclusive) pass the inspection? Part c: For what proportion of groups will exactly 3 trucks fail the inspection? Part d: Find the mean and the standard deviation of the random variable X

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

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

b. x + 1

step-by-step explanation:

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when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: