1)Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. I

Question

1)Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.41 ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains between 12.31 and 12.37 ounces.

2) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 470 seconds and a standard deviation of 60 seconds. Find the probability that a randomly selected boy in secondary school will take longer than 332 seconds to run the mile.

Explanation / Answer

Solution:

We need Z for 12.31 and 12.37
Z(12.31) = (12.31-12.41)/0.04 = -2.5
Z(12.37) = (12.37-12.41)/0.04 = -1
Prob(-2.5 < z < -1) from a table is:
0.1524

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