Answer to Question #222511 in Statistics and Probability for Charles Lewis

Question

• A steel mill produces alloy sheets used for the bodies of automobiles. The mill produces sheets with an average thickness of 0.517 inches and a standard deviation of 0.037 inches. A new car model requires alloy sheets between 0.495 and 0.525 inches thick. What percentage of the sheets made by the mill will be suitable for the new car model? Explain your answer. (75 words, or 1 paragraph)

Answer 1

Solution

Given that,

$\mu$ = 0.517

$\sigma$ = 0.037

So,

$P(0.495 < x < 0.525)$

$P(\frac{0.495-0.517}{0.037} < \frac{x-\mu}{\sigma}<\frac{0.525-0.517}{0.037})$

= $P(\frac{-0.02}{0.037}<z<\frac{0.01}{0.037})$

= $P(-0.54<z<0.27)$

= $P(z<0.27)-P(z<-0.54)$

= $0.6.64-0.2946$

= $0.3118$

= 31.18 %