Answer:
D
Step-by-step explanation:
using the definition of n =
where n! = n(n- 1)(n - 2)......× 3 × 2 × 1
here n = 7 and r = 4, hence
7
=
= ← cancel 3 × 2 × 1 leaving
7 = 7 × 6 × 5 × 4 = 840 → D
0.729 rounded by the nearest tenth
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.