Question

The distribution of claim amounts is normal with a mean of $1,500. The probability that a claim exceeds $5,000 is .015. Calculate in what range the standard deviation (o) of the distribution falls. Possible Answers A 0 <1,600 B 1,600 <0 < 1,625 C 1,625 <o<1,650 D 1,650 <o<1,675 BOX 1,675

Answer 1

P(X > 5000) = 0.015

or, P((X - $\mu$ )/$\sigma$ > (5000 - $\mu$ )/$\sigma$) = 0.015

or, P(Z > (5000 - 150 0)/$\sigma$) = 0.015

or, P(Z < (5000 - 1500)/$\sigma$) = 0.985

or, (5000 - 1500)/$\sigma$ = 2.17

or, $\sigma$ = (5000 - 1500)/2.17

or, $\sigma$ = 1612.9

Option – B)1,600 <o<1, 625