Pepsi uses six-sigma technique to evaluate whether its 12 oz Gatorade has consistent weight. Pepsi took a sampling of 1000 12 oz Gatorade and found out that the average weight was 11.58 oz with a standard deviation of 0.3 oz. Pepsi considers a tolerance of ± 5% from 12 oz acceptable.
a). What is the percentage of 12 oz Gatorade that meets the specification?
b). What are the percentages of 12 oz Gatorade that are considered “overweight” and “underweight”?
c). If Pepsi improves its production process, and samples another 1000 bottles and finds a average weight of 12 oz with a standard deviation of 0.2 oz. What is the % of 12 oz Gatorade that meets the specification? What quality standard does this new process achieve (in terms of number of “sigma”)?
d) Following c, what is the standard deviation that Pepsi needs to achieve in order to achieve the 6-sigma standard without having to change the specification?
2. If x is normally distributed with mean μ and standard deviation σ=5, and given that the probability that x is less than 34 is 0.0228. Find the value of μ.
3. A lightbulb has a normally distributed light output with mean 6000 end foot-candles and standard deviation of 100 end foot-candles. Find a lower tolerance limit such that only 0.2% of the bulbs will not exceed this limit.