Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 127.3-cm and a standard deviation of 1.7-cm.

Find the proportion of steel rods with lengths between 130.7 cm and 132.2 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

µ =    127.3              
σ =    1.7              
we need to calculate probability for ,                  
P (   130.7   < X <   132.2   )  
=P( (130.7-127.3)/1.7 < (X-µ)/σ < (132.2-127.3)/1.7 )                  
                  
P (    2.000   < Z <    2.882   )   
= P ( Z <    2.882   ) - P ( Z <   2.00   ) =   
0.9980   -    0.9772   =    0.0208   (answer)