What is the circumference of a circle with radius pi?
1 answer:
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Answer:
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".
Let X the random variable that represent interest on this case, and for this case we know the distribution for X is given by:
And let represent the sample mean, the distribution for the sample mean is given by:
On this case
Solution to the problem
We want this probability:
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:
No, Yes, No, Yes
using the laws of exponents
(1)
()³ =
4³ × 4³ =
≠
→ No
(2)
()^4 =
×
=
→ Yes
(3)
= (6 × 3 )^8 =
×
≠
×
→ No
(4)
= (4 × 5 )³ = 4³ × 5³ → Yes