# Statistics

**Question description**

2. A brewery filling machine is adjusted
to fill quart bottles with a mean of 32 oz of ale, and a **variance** of
0.003 . Periodically, a bottle is checked and amount of ale is
noted. Assuming that the amount of ale is NORMALLY DISTRIBUTED, what is
the probability that the next randomly checked bottle contains more than
32.03oz?

4. The student body of a college is composed of 50% females. Does a random sample of students (30 male, 20 female) from an introduction to chemistry class show sufficient evidence to reject the hypothesis that the proportion of females who take the chemistry class is the same as the whole student body? Use alpha = 0.025 Complete THE 5 STEP Hypothesis TEST

3. There are laws about speeding, but Rachel thinks they are broken most of the time. For example, most of I75 has a posted speed limit of 70mph. Her dad is a police officer and lets her borrow a radar gun for her research. Rachel checks 16 cars and finds the average speed to be 72mph with a standard deviation of 4mph. TEST THE CLAIM that the mean rate of the cars is over the speed limit, use alpha = 0.05

a. Complete THE 5 STEP Hypothesis TEST

b. Using at your answer to part a, IF there were an error, what type would it be and what is the probability that it occurs?

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