Max has a monthly salary of $1,100 and also earns 7.5% commission on his sales. If Max had $43,000 in sales last month, what wer
2 answers:
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Answer:
(a) The probability mass function of <em>X</em> is:
(b) The most likely value for <em>X</em> is 1.32.
(c) The probability that at least two of the four selected have earthquake insurance is 0.4015.
Step-by-step explanation:
The random variable <em>X</em> is defined as the number among the four homeowners who have earthquake insurance.
The probability that a homeowner has earthquake insurance is, <em>p</em> = 0.33.
The random sample of homeowners selected is, <em>n</em> = 4.
The event of a homeowner having an earthquake insurance is independent of the other three homeowners.
(a)
All the statements above clearly indicate that the random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 4 and <em>p</em> = 0.33.
The probability mass function of <em>X</em> is:
(b)
The most likely value of a random variable is the expected value.
The expected value of a Binomial random variable is:
Compute the expected value of <em>X</em> as follows:
Thus, the most likely value for <em>X</em> is 1.32.
(c)
Compute the probability that at least two of the four selected have earthquake insurance as follows:
P (X ≥ 2) = 1 - P (X < 2)
= 1 - P (X = 0) - P (X = 1)
Thus, the probability that at least two of the four selected have earthquake insurance is 0.4015.
Let x, y and z denote the weighs of car X, car Y and car Z, respectively.
We know that car X weighs 136 more than car Z, this can be express by the equation:
We also know that Y weighs 117 pounds more than car Z, this can be express as:
Finally, we know that the total weight of all the cars is 9439, then we have:
Hence, we have the system of the equations:
To solve the system we can plug the values of x and y, given in the first two equations, in the last equation; then we have:
Now that we have the value of z we plug it in the first two equations to find x and y:
Therefore, car X weighs 3198 pound, car Y weighs 3179 pounds and car Z weighs 3062 pounds.