Answer to Question #191117 in Civil and Environmental Engineering for Joshua

Question

A construction laborer is asked to make stirrups for their project and notices that the average length of rebards he need to make is about 30 cm. He concludes that tge rebars have a standard deviation of 2 cm. Assuming that the lengtha are normally distributed, what percentage of the steel bars are between 29.30 and 33.50 cm?

Answer 1

Given that $\mu=30, \delta =2$

$P(29.30<x<33.50)$

$P( \frac{29.30-30}{2}< \frac{x- \mu}{ \delta}< \frac{33.50-30}{2})$

$P( \frac{-0.7}{2}< z< \frac{3.5}{2})$

$P( -0.35< z< 1.75)$

$P( z<1.75)-P( z<-0.35)$

$0.9599-0.3632$

$0.5967$

$59.67$ %