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.
= 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
P(M < 177.8 cm) = P(Z < (177.8 - 179)/0.69282)
= P(Z < -1.732)
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