Question

If the average of a normal distribution of losses is $5,000 and the standard deviation is $200 – 68% of values lie within one standard deviation.

What is the upper bound and lower bound for this range?

Similarly, 95% of values lie within 2 standard deviations.

What is the upper bound and lower bound for this range?

Answer 1

solution

(A)P( - 1< X < + 1) = 68%

P(5000 - 200< X < 5000 + 200) = 68%

P(4800 < X < 4800) = 68%

Answer = lower bound =4800 and upper bound =4800

(B)

P( - 2< X < + 2) = 95%

P(5000 - 400 < X <5000 + 400) = 95%

P(4600 < X < 5400) = 95%

Answer =lower bound= 4600 and upper bound=540