Discussion Board 8 Central Limit Theorem Sample Mean Distribution & Sample Proportion Distribution 1. The average calories consumed by a SDSU student during a day is 2,345 calories with a standard deviation of 380 calories. Use this information to answer the following questions: A. If you randomly select 40 SDSU students, what is the probability that the average number calories consumed during the day will be more than 2,250 calories? B. If you randomly select 150 SDSU students, what is the probability that the average number calories consumed during the day will be between 2,300 calories and 2,400 calories? 2. The proportion of an adult's diet that contains ultra processed foods is 57.6%. Use this information to answer the following questions: A. If you randomly select 60 adults, what is the probability that at most 54% of their diet contains ultra processed foods? B. If you randomly select 125 adults, what is the probability that at least 53% of their diet contains ultra processed foods? C. If you randomly select 200 adults, what is the probability that between 55% to 65% of their diet contains ultra processed foods? Discussion Board 9 Confidence Intervals Means (sigma known and unknown) & Proportions 1.You would like to estimate the average time an adult walk during the day. You randomly select 83 adults and get a sample mean of 26.1 minutes; the population standard deviation is known to be 5.3 minutes. A. Construct an 80% confidence interval for the average time an adult walk during the day (round final answer to 3 decimal places ex. 14.173 to 18.295). B. If you would like to have a margin of error of to be within 0.5 minutes (% minute) (using the same confidence from above), how many adults should be sampled? 2. You would like to estimate how much a single taxpayer that itemizes on their individual tax return Schedule A. You randomly select 65 single taxpayer that itemizes on their individual tax return Schedule A and get a sample mean of $17,641 with a standard deviation of $3,190. Construct a 95% confidence interval for the amount a single taxpayer that itemizes on their individual tax return Schedule A. A. Confidence value used for this problem (from table or chart ex. 80% Z-Value: 1.282 or 80% t- Value: 1.305) B. Construct a 95% confidence interval for the amount a single taxpayer that itemizes on their individual tax return Schedule A (round final answer to 2 decimal places (nearest penny) ex. $14.17 to $18.29). 3.You would like to estimate the proportion of taxpayers who apply for a 6 month extension to file taxes. You randomly select 280 taxpayers, and find that 48 apply for a 6 month extension to file taxes. A. Construct a 90% confidence interval to estimate the proportion of taxpayers who apply for a 6 month extension to file taxes. (Round your sample proportion to 4 decimal points as well as round your margin of error to 4 decimal points. For example: .14916 would be .1492 and this represents 14.92%. State the answer as an interval for example 27.36% to 31.43%). B. Using the same confidence level, you would like the margin of error to be 3%, how many customers should you sample