could any one help me solve this question? 0.0124 Selling only 12 policies incre
ID: 3132174 • Letter: C
Question
could any one help me solve this question?
0.0124
Selling only 12 policies increases the probability for a total loss, comparing to much smaller probability in case of large number of policies. The distribution of the mean claim is much more Normal when thousands of policies are sold and not only 12. Therefore the company has much more control over profit and losses when thousands of policies are sold. The law of large numbers says that for large number of policies, the average claim is equal to the mean of $250. Therefore the risk is much lower when thousands of policies are sold and not only 12. The average claim for 12 policies may be far different from the mean, so the risk of a disastrous loss is high. For thousands of policies the law of large numbers supplies protection against such lost.Explanation / Answer
STEP 1:
OPTION C: The law of large numbers says that for large number of policies, the average claim is equal to the mean of $250. Therefore the risk is much lower when thousands of policies are sold and not only 12. [ANSWER]
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STEP 2:
We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as
x = critical value = 270
u = mean = 250
n = sample size = 25000
s = standard deviation = 1000
Thus,
z = (x - u) * sqrt(n) / s = 3.16227766
Thus, using a table/technology, the right tailed area of this is
P(z > 3.16227766 ) = 0.000782701 = 0.0008 [answer, b]
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