Question

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 122.8-cm and a standard
deviation of 0.6-cm. For shipment, 6 steel rods are bundled
together.

Find the probability that the average length of a randomly selected
bundle of steel rods is less than 122.7-cm.

*P*(*M* < 122.7-cm) =

Enter your answer as a number accurate to 4 decimal places. Answers
obtained using exact *z*-scores or *z*-scores rounded
to 3 decimal places are accepted.

Answer #1

Solution :

Given that ,

mean = = 122.8

standard deviation = = 0.6

n = 6

m = 122.8

m = / n = 0.6 / 6=0.2449

P(M < 122.7) = P[(M - m ) / m < (122.7 -122.8) /0.2449 ]

= P(z < -0.408)

Using z table

=0.3416

probability=0.3416

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