Final answer:
The upper control limit on a p-chart with pbar = 0.60 and a sample size of 20 is determined using the formula, incorporating the standard deviation of the proportion and the Z value. The UCL is calculated to be approximately 0.815, which rounds to option B, 0.80.
Step-by-step explanation:
To find the upper control limit (UCL) on a p-chart, we use the formula UCL = pbar + Z * sqrt[(pbar * (1 - pbar) / n)], where pbar is the overall average value, Z is the z-value from the standard normal distribution, and n is the sample size. Given that pbar is 0.60 and the sample size (n) is 20, we must find the appropriate Z value.
Using a standard normal probability table or calculator, we find Z for the upper control limit, commonly Z0.025.
The Z value corresponding to the 95th percentile (leaving 5% in the upper tail) is approximately 1.96.
Plug these values into the formula to get the UCL.
First, calculate the standard deviation of the proportion: sqrt[(0.60 * (1 - 0.60) / 20)] = 0.1095.
Next, calculate the UCL: 0.60 + (1.96 * 0.1095) = 0.60 + 0.2146 = 0.8146.
Therefore, the UCL is approximately 0.815, which corresponds to option B, 0.80, when rounded to two decimal places.