The first question, first of all, the death rate of 1W insured is 0.006, and the number of deaths is a random variable X that obeys binomial distribution.
B( 10000, 0.006) n= 10000, p=0.006 Now consider the approximate calculation of binomial distribution. Because np=60 is much larger than 10 and does not satisfy Poisson approximation, we choose normal approximation. The formula is N(np, np( 1-p).
The probability that X follows the normal distribution N (60 60,59.64) through normal approximation can be obtained by using the formula X-U/ Sigma (this symbol can't be typed out), finding the FAI value, and then checking the standard normal.
The square of this normal distribution u =60 sigma is equal to 59.64. Sigma equals the square root of 59.64.
In case of loss, the compensation amount is greater than 12W, and the death toll at this time is 120. FAI (square root of (120-60)/59.64). Obviously, this FAI (considerable) = 1, and the probability of FAI3.9 is already equal to 1, so the probability of death toll exceeding 120 = 1- 1=0.
Then calculate the probability that the profit is not less than 4W yuan. At this time, the compensation amount should not exceed 8W, and the death toll should not exceed 80.
FAI (the square root of (80-60)/59.64) can be found that the probability of more than 80 deaths should be calculated by1-FAI (the square root of (80-60)/59.64).
Similarly, the probability that the profit is not less than 6W yuan is FAI (60-60)/the square root of 59.64). At this time, X=0 is the peak of standard normal distribution, and FAI(0) is a special value of 0.5.
Similarly, the probability that the profit is not less than 8W yuan is FAI (40-60)/the square root of 59.64). At this time, the calculation of FAI (negative number) only needs to use 1-FAI (the reciprocal of this negative number) to calculate.