Question

Suppose certain coins have weights that are normally distributed with a mean of 5.414 g and a standard deviation of 0.069 g. A vending machine is configured to accept those coins with weights between 5.294 g and 5.534 g. a. If 280 different coins are inserted into the vending​ machine, what is the expected number of rejected​ coins? The expected number of rejected coins is ---Round to the nearest integer

Answer 1

(A) Given that

mean = 5.414

sd = 0.069

coin is rejected only when it is outside the range of 5.294 g and 5.534 g

so, probability of falling outside the range of 5.294 g and 5.534 g is given as '

P(outside the range of 5.294 g and 5.534 g) = 1 -normalcdf

setting lower = 5.294, upper= 5.534, mean= 5.414 and sd = 0.069

= 1- normalcdf(5.294, 5.534, 5.414, 0.069)

= 1 - 0.918

= 0.082

so, required number of rejected coins = n*p

setting n = 280 and p = 0.082

we get

Expected number = 280*0.082 = 23