Question

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.

Answer 1

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