Form a sequence that has two arithmetic means between -1 and 59.
2 answers:
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We are told that f(x) = x + 2. We want to find .
Squaring f(x) on one side means we square x + 2 on the other.
So,
f(x) = x + 2
(f(x))² = (x + 2)²
= (x + 2)(x + 2)
We can use FOIL to square x + 2. The first terms multiply to x², the outside terms to 2x, the inside terms to 2x and the last terms to 4.
= x² + 2x + 2x + 4
= x² + 4x + 4
So [f(x)]² = x² + 4x + 4
Answer:
First part
And for this case we can use the z score formula given by:
And using this formula we got:
And we can use the normal standard table or excel and we got:
Second part
For the other part of the question we want to find the following probability:
And using the score we got:
And we can find this probability with this difference:
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 data of a population, and for this case we know the distribution for X is given by:
Where and
First part
And for this case we want this probability:
And for this case we can use the z score formula given by:
And using this formula we got:
And we can use the normal standard table or excel and we got:
Second part
For the other part of the question we want to find the following probability:
And using the score we got:
And we can find this probability with this difference: