A ball is released at a height of 8 inches to roll inside a half - cylinder. It rolls to a height of 2 inches on the other side
of the cylinder on roll 1. each time it rolls up a side of the cylinder, the ball reaches a point that is 1/4 as high as it had reached on the other side. This explicit formula models the height of the ball, in inches, the nth time it rolls up a side of the cylinder. A. 1 inch B. 1/8 inch C. 1/4 inch D. 1/2inch
1 answer:
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Answer:
a)
And we can find this probability with the following difference:
b)
And we can find this probability with the following 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".
Part a
Let X the random variable that represent the diameters of a population 1, 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 following difference:
Part b
And we can find this probability with the following difference: