A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 263.6 cm and a standard
deviation of 0.5 cm. For shipment, 27 steel rods are bundled
together.
Find the probability that the average length of a randomly selected
bundle of steel rods is less than 263.6 cm.
P(¯xx¯ < 263.6 cm) =
Enter your answer as a number accurate to 4 decimal places. Answers
should be obtained using zz scores rounded to two decimal
places.
Solution :
Given that,
mean = = 263.6
standard deviation = = 0.5
n = 27
= 263.6
= ( /n) = (0.5 / 27 ) = 0.0962
P ( < 263.6 )
P ( - /_{}) < ( 263.6 - 263.6 / 0.0962 )
P ( z < 0 / 0.0962 )
P ( z < 0.00 )
Using z table
= 0.5000
Probability = 0.5000
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