Which form of a quadratic function is easiest to use when finding the maximum or minimum value of the function?
2 answers:
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Answer:
And we can find this probability with the normal standard distirbution or excel and we got:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the lenghts of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability with the normal standard distirbution or excel and we got:
Answer:
a) In the interval of [1980,1983].
b) In the interval of [1991, 1996].
Step-by-step explanation:
Fuel efficiency:
The fuel efficiency, for the cars, in x years after 1980, is given by:
15.9 is the fuel efficiency in 1980.
a. In what years was the average fuel efficiency for cars less than 17 mpg (in interval form)?
From 1980 to:
3.06 = 1980 + 3 = 1983. So
In the interval of [1980,1983].
b. In what years was the average fuel efficiency for cars more than 20 mpg (in interval form)?
From x until 1996.
11.38 = 1980 + 11 = 1991. So
In the interval of [1991, 1996].