A company produces steel rods. The lengths of the steel rods are normally distri

Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 229.3-cm and a standard deviation of 0.6-cm. For shipment, 24 steel rods are bundled together.

Find the probability that the average length of the rods in a randomly selected bundle is between 229.3-cm and 229.6-cm.
P(229.3-cm < ¯¯¯XX¯ < 229.6-cm) =  Round to 4 decimal places.

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

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 229.3-cm and a standard deviation of 0.6-cm. For shipment, 24 steel rods are bundled together. Find the probability that the average length of the rods in a randomly selected bundle is between 229.3-cm and 229.6-cm. P(229.3-cm

Explanation / Answer

Solution:-   mean = 229.3-cm , a standard deviation = 0.6-cm n =24

P(229.3 < X < 229.6) = P((229.3 - 229.3)/(0.6/sqrt24) < Z < (229.6 - 229.3)/(0.6/sqrt24))

=  P(0 < Z < 2.45)

=  0.4929

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