Which best proves why the expressions 4 (x + 3) + 2 x and 6 (x + 2) must be equivalent expressions?
1 answer:
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Answer:
a) The value corresponding to surviving the year is -$176.
The value corresponding to not surviving the year is $109,824.
b) From the point of view of the insurance company, the expected value of the policy is $22.
As the expected value is positive, the company is expected to make profits from many such policies. According to the Law of large numbers, increasing the amount of policies, the deviation from the expected result will decrease. If the amount of policies is big enough, a profit is guaranteed for the company.
Step-by-step explanation:
a. From the perspective of the 29-year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving?
The two events and the montery values for each are:
1) Surviving. The probability is 0.9986 and the monetary value is -$176.
2) Not surviving. The probability is (1-0.9986)=0.0014 and the monetary value is ($110,000-$176)=$109,824.
b. If the 29-year-old male purchases the policy, what is his expected value? Can the insurance company expect to make a profit from many such policies? Why?
The expected value can be calculated from the possible outcomes multiplied by its probabiltity of occurrence.
From the 29-year-old male, the expected value is:
The expected value for the company is the negative of the expected value of the client, so it has a expected value of $22 per person.
As the expected value is positive, the company is expected to make profits from many such policies. According to the Law of large numbers, increasing the amount of policies, the deviation from the expected result will decrease. If the amount of policies is big enough, a profit is guaranteed for the company.
Answer:
Bella's score on the exam is 87.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Arturo's score on the exam is 75
His score is Z standard deviations above the mean
Bella’s score is 1.5 standard deviations above Arturo’s score.
So Bella's z-score is 1.5 + 0.625 = 2.125.
Her score is the value of X when Z = 2.125. So:
Bella's score on the exam is 87.