Question

The car contains 50,000 rods. Claude Ong, manager of Quality Assurance, directs his crew measure the lengths of 100 randomly selected rods. If the population of rods have a mean length of 120 inches and a standard deviation of 0.05 inch, the probability that Claude's sample has a mean less than 119.985 inches is
A) 0.9974
B) 0.0026
C) 0.4987
D) 0.0013
E) 0.0030

Answer 1

Answer: D) 0.0013

Step-by-step explanation:

Let x be the random variable that represents the lengths of rods.

As pr given , we have

n=100 , $\mu=120\ inches$  $\sigma=0.05\ inch$

z-score : $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For x= 119.985 inches , we have

$z=\dfrac{119.985 -120}{\dfrac{0.05}{\sqrt{100}}}=-3$

Using the standard z-table , we have

The probability that Claude's sample has a mean less than 119.985 inches is

$P(z<-3)=1-P(z<3)\\\\=1-0.9986501\\\\=0.0013499\approx0.0013$

Hence, the probability that Claude's sample has a mean less than 119.985 inches is 0.0013.