A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 108.7-cm and a standard deviation of 0.6-cm. For shipment, 22 steel rods are bundled together.

Find the probability that the average length of rods in a randomly selected bundle of steel rods is less than 109.1-cm.

Round to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.

Question

Jayvion Moody

Mathematics

17 January, 10:03

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 108.7-cm and a standard deviation of 0.6-cm. For shipment, 22 steel rods are bundled together.

Find the probability that the average length of rods in a randomly selected bundle of steel rods is less than 109.1-cm.

Round to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.

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Answers (1)

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Iyana Moss · Answer 1

Let x be the lengths of the steel rods and X ~ N (108.7, 0.6)

To get the probability of less than 109.1 cm, the solution is computed by:

z (109.1) = (X-mean) / standard dev

= 109.1 - 108 / 0.6

= 1.1/0.6

=1.83333, look this up in the z table.

P (x < 109.1) = P (z < 1.8333) = 0.97 or 97%