DETAILS ASWSBE13 7.E.019. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER You may need to use the appropriate appendix table or technology to answer this question. A population has a mean of 800 and a standard deviation of 200. Suppose a sample of size 400 is selected and x is used to estimate #. (Round your answers to four decimal places.) (a) What is the probability that the sample mean will be within 15 of the population mean? (b) What is the probability that the sample mean will be within +10 of the population mean? Need Help? Read It Watch It DETAILS ASWSBE13 7.E.041.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 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 800 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. 0.144 0.157 0.17 0.183 0.196 -1.83 -0.83 0.17 1.17 2.17 -0.026 -0.013 0 0.013 0.026 -0.013 0 0.013 0.026 0.039 (b) What is the probability that the sample proportion will be within 10.02 of the population proportion? (Round your answer to four decimal places.) ) Answer part (b) for a sample of 1,600 households. (Round your answer to four decimal places.) Need Help? Read It Master It 3. DETAILS ASWSBE13 7.E.051.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER You may need to use the appropriate appendix table or technology to answer this question. market research firm conducts telephone surveys with a 42% historical response rate. What is the probability that in a new sample of 400 telephone numbers, at least 150 individuals will cooperate and respond to the questions? In other words, what is the probability that the sample proportion will be at least 150 400 - = 0.375? (Round your answer to four decimal places.)