Week 10 Use the Textbook Materials for Chapter 6. For Chapter 6, Section 3, watch the Lecture Video and the 3 Exercise Videos. Also, read Which Z Formula to Use (posted with Homework in Assignments). Then, do the following problems. Use the Z table in your textbook (pp. 782 - 783) to look up the probabilities associated with the z-scores you compute. Since you can only look up z-scores in your table with two decimal places, you must round any z-scores you compute with more than two decimal places. So, if you compute a z-score of 1.2664, you would look up 1.27 (not 1.26). Show your work for the problems where indicated and put your answer in the final column. PROBLEM WORK ANSWER 1. A tropical city has a temperature which is normally distributed. The average temperature is 100 degrees F with a standard deviation of 10 degrees. 1a. What is the probability that the temperature on a randomly chosen day is more than 95 degrees? 1b. If a sample of 25 days is selected, what is the probability that the mean temperature is less than 95 degrees? 1c. If a sample of 25 days is selected what is the probability that the mean temperature is between 95 and 97.5 degrees? 1d. If a sample of 25 days is selected what is the probability that the mean temperature is above 102.2 degrees? 1e. If a sample of 25 days is selected, there is a 65% chance that the mean temperature is above what value? 2. 72% of the households in a small town own at least one smart phone. 2a. If we randomly sample 25 households at a time, and ask whether they own a smart phone, what will be the mean and the standard deviation of the distribution of sample proportions? 2b. Will the distribution in 2a be approximately normal in shape? [Support your answer with numerical guidelines.] 3. A supermarket cashier spends an average of 3.10 minutes with each shopper with a standard deviation of .40 minutes. 3a. What is the probability that the time spent with a customer is at least 3 minutes? 3b. A random sample of 64 customers is selected. There is an 85% chance that the sample mean is less than how many minutes? 3c. In order to answer 3a, do we need to make the assumption that the population (of amount of time spent per customer) was normally distributed? Explain. In order to answer 3b, do we need to make the assumption that the population (of amount of time spent per customer) was normally distributed? Explain