Question

A scientist wishes to estimate the mean breaking strength of a certain type of steel rod within 3.0 psi with 95% confidence. Based on experience with a similar type of steel, she believes the standard deviation is approximately 15.0 psi in individual breaking strengths. How many steel rods should she test?

Answer 1

Answer:97 rods

Step-by-step explanation:

The number of steel rods for 95% confidence level

$n=\left ( \frac{Z_\frac{\alpha }{2}\times \hat{\sigma }}{E} \right )^2$

$Z_\frac{\alpha }{2}=1.96$

E=3

$\hat{\sigma }=15$

Substituting values

$n=\left ( \frac{1.96\times 15}{3}\right )^2$

$n=96.04\approx 97$

Thus 97 rods is tested