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Alexxx [7]
3 years ago
10

The car contains 50,000 rods. Claude Ong, manager of Quality Assurance, directs his crew measure the lengths of 100 randomly sel

ected 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
Mathematics
1 answer:
pshichka [43]3 years ago
3 0

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

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

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