Probability of soft-drink machine

[superwolf]

A soft-drink machine discharges an average of 200 ml per cup, with a standard deviation of 15 ml. What is the probability that a cup contains between 191 and 209 ml?


Attempt:

$$Z_1 = \frac{190.5-200}{15} = -0.63$$

$$Z_2 = \frac{209.5-200}{15} = 0.63$$

The table in my book "Areas under the normal curve", gives P = 0.7357-0.2643 = 0.4714

Correct answer (according to the same book): 0.4514

Are my continuity corrections wrong?

 

[ToxicBug]

I don't think that you need a continuity correction here, unless the problem specifies that the machine can only dispense discrete amounts.

(209 - 200)/15 = .6

P(Z < .6) = .7257
.7257 - (1-.7257) = .4514