Hi Bailey,
The empirical rule is also called the 68-95-99.7 rule, which means that 68% of data falls within one standard deviation of the mean, 95% falls within two, and 99.7% falls within three. Do as the problem suggested and sketch the bell curve--I can't really show it here, but the mean of 60 will be dead-center. One standard deviation on each side goes from 54 to 66 oz. Two go from 48 to 72. So, for part b:
b) 95% of distribution is covered by 48 to 72 oz. range, but your question asked about 42 to 72. 42 takes us one additional standard deviation back in the negative direction, so this is the 99.7 range, 4.7 percentage points above 95. BUT remember that this is only one end, so we have to divide this by two. 4.7/2=2.35.
95+2.35=
97.35%
c) This is similar. You want weights above 54. You know from the rule that 68% of weights fall between 54 and 66 oz. This leaves you with 32% of the data left to account for, but again, remember that you want only half of that because the question specified above 54. Thus the calculation is:
68+(32/2)=
68+16=
84%
I hope this helps. I recommend getting used to that bell-curve sketch with 68, 95, and 99.7 marked off. I also recommend getting used to the z-tables.
