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2 answers:
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9514 1404 393
Answer:
(a) none of the above
Step-by-step explanation:
The largest exponent in the function shown is 2. That makes it a 2nd-degree function, also called a quadratic function. The graph of such a function is a parabola -- a U-shaped curve.
The coefficient of the highest-degree term is the "leading coefficient." In this case, that is the coefficient of the x² term, which is 1. When the leading coefficient of an even-degree function is positive, the U curve has its open end at the top of the graph. We say it "opens upward." (When the leading coefficient is negative, the curve opens downward.)
This means the bottom of the U is the minimum value the function has. For a quadratic in the form ax²+bx+c, the horizontal location of the minimum on the graph is at x=-b/(2a). This extreme point on the curve is called the "vertex."
This function has a=1, b=1, and c=3. The minimum of the function is where ...
x = -b/(2·a) = -1/(2·1) = -1/2
This value is not listed among the answer choices, so the correct choice for this function is ...
none of the above
__
The attached graph of the function confirms that the minimum is located at x=-1/2
_____
<em>Additional comment</em>
When you're studying quadratic functions, there are few formulas that you might want to keep handy. The formula for the location of the vertex is one of them.
Answer:
a) 0.3408 = 34.08% probability that at least one accident will occur on a blizzard day on a 25 mile long stretch of highway.
b) 0.0879 = 8.79% probability that two out of these six blizzard days have no accident on a 25 mile long stretch of highway.
c) 0.4493 = 44.93% probability of no damaging accidents requiring a insurance claims on an 80 mile stretch of highway.
Step-by-step explanation:
We have the mean for a distance, which means that the Poisson distribution is used to solve this question. For item b, the binomial distribution is used, as for each blizzard day, the probability of an accident will be the same.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
Suppose one traffic accident is expected to occur in each 60 miles of highway blizzard day.
This means that , in which 60 is the number of miles.
(a) What is the probability that at least one accident will occur on a blizzard day on a 25 mile long stretch of highway?
, and thus,
This probability is:
In which
0.3408 = 34.08% probability that at least one accident will occur on a blizzard day on a 25 mile long stretch of highway.
(b) Suppose there are six blizzard days this winter. What is the probability that two out of these six blizzard days have no accident on a 25 mile long stretch of highway?
Binomial distribution.
6 blizzard days means that
Each of these days, 0.6592 probability of no accident on this stretch, which means that .
This probability is P(X = 2). So
0.0879 = 8.79% probability that two out of these six blizzard days have no accident on a 25 mile long stretch of highway.
(c) If the probability of damage requiring an insurance claim per accident is 60%, what is the probability of no damaging accidents requiring a insurance claims on an 80 mile stretch of highway?
Probability of damage requiring insurance claim per accident is of 60%, which means that the mean is now:
80 miles:
This means that . So
The probability of no damaging accidents is P(X = 0). So
0.4493 = 44.93% probability of no damaging accidents requiring a insurance claims on an 80 mile stretch of highway.