Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 179-cm and a standard deviation of 2.4-cm. For shipment, 12 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is less than 177.8-cm.
P(M < 177.8-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

= 179 cm

= 2.4 cm

n = 12

According to Central Limit Theorem, the distribution of sample mean will be approximately normal.

P( < A) = P(Z < (A - )/)

= = 179 cm

=

=

= 0.69282

P(M < 177.8 cm) = P(Z < (177.8 - 179)/0.69282)

= P(Z < -1.732)

= 0.0416