Question

Suppose certain coins have weights that are normally distributed with a mean of 5.938 g and a standard deviation of 0.078 g. A vending machine is configured to accept those coins with weights between 5.848 g and 6.028 g.

If 260 different coins are inserted into the vending​ machine, what is the expected number of rejected​ coins?

Answer 1

µ =    5.938                              
σ =    0.078                              
we need to calculate probability for ,                                  
P (   5.848   < x <    6.028   )                  
=P( (5.848-5.938)/0.078 < (X-µ)/σ < (6.028-5.938)/0.078 )                                  
                                  
P (    -1.154   < Z <    1.154   )                   
= P ( Z <    1.154   ) - P ( Z <   -1.154   ) =    0.8757   -    0.1243   =    0.7514

Probability of rejecting coins = 1 - 0.7514 = 0.2486

expected number of rejected​ coins = 260*0.2486 = 64.626 ≈ 65 coins (answer)