Three Flags, a Small Independent Water Park, Collects Data on the Number

Question

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The Answer is To calculate the overall proportion of visitors, we first need to find the total number of out-of-state plates over the 10 days. Adding up the numbers gives us a total of 224 out-of-state plates. To find the overall proportion, we divide this total by the total number of cars, which is 100 cars per day multiplied by 10 days, giving us 1000 cars. So, the overall proportion of visitors is 224/1000 = 0.224 or 22.4%.

To calculate the standard deviation of proportions, we can use the formula for the standard deviation of a sample proportion, which is given by the square root of (p*(1-p)/n), where p is the proportion and n is the sample size. Plugging in the values, we get the standard deviation to be sqrt(0.224*(1-0.224)/10) = 0.033 or 3.3%.

B: Using ± 3-sigma limits, we can calculate the LCL and UCL for these data. The LCL (Lower Control Limit) is given by the overall proportion - 3 times the standard deviation, and the UCL (Upper Control Limit) is given by the overall proportion + 3 times the standard deviation. Plugging in the values, we get the LCL to be 0.224 - 3*0.033 = 0.125 or 12.5%, and the UCL to be 0.224 + 3*0.033 = 0.323 or 32.3%.

C: Based on the process control limits, we can say that the proportion of visitors with out-of-state plates is within control limits, indicating that the process is stable and in control. However, the variation in the proportions is relatively high, as indicated by the standard deviation. This suggests that there may be some inconsistency in the number of out-of-state visitors from day to day, and further investigation may be needed to understand and potentially improve this variability.

Three Flags, a Small Independent Water Park, Collects Data on the Number

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