a company produces steel rods

Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 125.7-cm and a standard deviation of 1.5-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 between 124.1-cm and 124.7-cm.

P(124.1-cm < M < 124.7-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

P(124.1 < M < 124.7)

convert limits of above inequality to be around z using standardized z score: (x - mean)/(STD/sqrt(sample size))

where mean is 125.7, SD = 1.5 and sample size is 6.

P(124.1 < M < 124.7) =

P((124.1 - 125.7)/(1.5/Sqrt(6)) < z < (124.7 - 125.7)/(1.5/sqrt(6)) =

P(-2.61 < z < -1.63) =

P(z< -1.63) - P(z < -2.61) =

0.0516 - 0.0045 =

0.0471