Exercise
ABy Admin
May 07'23
Answer
Solution: D
The probability that a randomly selected cable will not break under a force of 12,400 is
[[math]]\operatorname{P}(Y \gt 12, 400) =\gt P[ Z (12, 400 − 12, 432) / 25 =−1.28] =0.9. [[/math]]
The number of cables, [math]N[/math], that will not break has the binomial distribution with [math]n = 400 [/math] and [math]p = 0.9[/math]. This can be approximated by a normal distribution with mean 360 and standard deviation 6. With the continuity correction,
[[math]]\operatorname{P}( N ≥ 349) =≥ P[ Z (348.5 − 360) / 6 = −1.9167] = 0.97. [[/math]]
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.