Someone Please help me answer this question.
2 answers:
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Answer:
a)
b)
c)
d)
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".
Part a
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where and
We select a random sample of n=36. And from the central limit theorem we know that the distribution for the sample is given by:
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:
Part b
For this case we want this probability:
And we can find this probability on this way:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
Part c
If we apply this formula to our probability we got this:
Part d
For this case we want this probability:
And we can find this probability on this way:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
Answer:
The required inequality is: 12 ≤ 3x < 21
Step-by-step explanation:
We are given: three times a number is greater than or equal to 12 and less than 21
We need to answer following questions:
1) The inequality translated in numerical form
Let number = x
12 ≤ 3x < 21
2) Your work solving the inequality
We need to find value of x. Divide the inequality by x
4 ≤ x < 7
3) The solution graphed on a number line
It is shown in figure attached.
4) The solution in set notation
The set notation is: Considering x belongs to natural numbers N
{∀ x|x∈N, 4 ≤ x < 7}
5) The solution in interval notation
The interval notation is: [4,7)
because we have 4 less than equal to x and x is less than 7
