Tutorial Exercise You may need to use the appropriate appendix table or technology to answer this question The Food Marketing Institute shows that 17 of households spend more than 100 per week on groceries Assume the population proportion is p 0 17 and a sample of 900 households will be selected from the population a Show the sampling distribution of p the sample proportion of households spending more than 100 per week on groceries b What is the probability that the sample proportion will be within 0 02 of the population proportion c Answer part b for a sample of 1 800 households Step 1 a Show the sampling distribution of p the sample proportion of households spending more than 100 per week on groceries Recall that a sampling distribution of p is a discrete probability distribution but can be approximated by a normal distribution when np 5 and n 1 p 5 where n is the sample size and p is the population proportion Here it is given that p 0 17 There is a sample of 900 households so n np n 1 p 0 17 nd n 1 1 0 17 0 5 the normal approximation Select be used Find the values of np and n 1 p