# Thread: normal distribution

1. ## normal distribution

A soft-drink bottler has a machine that fills 375 mL cans. The machine is designed to place 377 mL in the can with a standard deviation of 0.5 mL.
a.What percent of cans will have less than 376 mL?
b.What percent of cans will have less than 375.5 mL?
c.Cans that contain less than 376 are rejected. In a production run of 50,000, how many cans are rejected?

2. Originally Posted by terminator
A soft-drink bottler has a machine that fills 375 mL cans. The machine is designed to place 377 mL in the can with a standard deviation of 0.5 mL.
a.What percent of cans will have less than 376 mL?
b.What percent of cans will have less than 375.5 mL?
c.Cans that contain less than 376 are rejected. In a production run of 50,000, how many cans are rejected?
a. z = $\displaystyle \frac{376-377}{0.5}$
z = -2
P(z <-2) = 2.275% (from normal tables)

b. z = $\displaystyle \frac{375.5-377}{0.5}$
z = -3
P(z <-3) = 0.15% (from normal tables)

c. 2.275% are rejected
50000 x 2.275% = 1375 can rejected

3. thanks. really,really helpful