The National Park Service observers also reported that 3% of whale-ship encounters occurred within 985 feet of the bow of the ship. Let p be the sample proportion of encounters where a whale came within 985 feet of the bow in a sample of 85 encounters. Part A: Assuming p = 0.03, calculate the mean and standard deviation of the sampling distribution of p Mean = Standard deviation (rounded to four decimal places) = Part B: Assuming p = 0.03 and n = 85, use the DCMP Normal Distribution tool (https://dcmathpathways.shinyapps.io/NormalDist/) to calculate the probability that p falls between 0 and 0.06. Round to four decimal places. Part C: Use the DCMP Sampling Distribution of the Sample Proportion tool (https://dcmathpathways.shinyapps.io/SampDist Prop/=) to simulate 10,000 sample proportions when p = 0.03 and n = 85. Use the simulation results to find the proportion of samples where p falls between 0 and 0.06. Make sure to click the box labeled "Find Probability for Samp. Dist." Part D: Explain why the probabilities calculated in Parts B and C are so different. Hint Are the conditions met to use the normal approximation to the sampling distribution of p in this case