Suppose the force acting on a column that helps to support a building is normally distributed with mean $15.0$ kips and standard deviation $1.25$ kips. What is the probability that the force

• (a) Is at most $17$ kips?
• (b) Is between $10$ and $12$ kips?
• (c) Differs from $15.0$ kips by at most $2$ standard deviations?
   

Remark:

1kips=1千磅=1000磅=453.59237千克(kg)

假设有助于支撑建筑物的作用在柱上的力满足均值为 15千磅, 标准差为 1.25千磅的正态分布.

求

• (a) 力至多为 $17$ 千磅的概率是多少?
• (b) 力在 $10$ 千磅和 $12$ 千磅之间的概率是多少?
• (c) 力和 $15$ 千磅之差在 $2$ 个标准差之间的概率是多少?