A system of regular payments for when something bad happens
1 answer:
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Answer:
a)
b)
c)
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:
a. Find P(x < 6). P(x < 6) = (Round to four decimal places as needed.)
In order to find this probability we can use the z score given by this formula
And if we use this we got this:
b. Find P(8 < x < 10) = (Round to four decimal places as needed.)
c. Find the value a for which P(x < a) = 0.2. (Round to two decimal places as needed.)
For this case we can use the definition of z score given by:
First we need to find a z score that accumulates 0.2 of the area on the left tail, and the z score on this case is z=-0.842. and using this z score we can solve for x like this:
And if we solve for x we got:
And that would be the value required for this case.