Homework Problems: Please handwrite and turn in solutions to the following problems. These problems are worth 20 points each. Please include a properly labeled and shaded figure for each problem. You may use Python to obtain probabilities. Put your work in a single.py file with comments labeling your work. 1. You will find a .csv file on eCampus representing patient body temperatures at a hospital on a particular day. The data is organized into two columns: patient temperature, patient age. Using code snippets available from the class lecture material, perform the following tasks with this data: a. Read the data into Python b. Determine the mean, mode, median, variance, and standard deviation for the patient temperatures. Please print from Python and write on your solution page. c. Determine the mean, mode, median, variance, and standard deviation for the patient ages. Please print from Python and write on your solution page. i. Note: You can try to find the mode of the age data, but Python will return and error. There are two equally-frequent values in the data set. d. Plot a histogram of the temperature data. Please include a title and proper axes labels. 2. FIQ scores are normally distributed with a mean of 100 and a standard deviation of 5, what is the probability that a person selected at random will have an IQ of 110 or greater? 3. The amount of hot chocolate dispensed by a hot chocolate machine is normally distributed with a mean of 16.0 oz. and a standard deviation of 2 oz. If the cups hold 18.0 oz., what is the probability that a selected cup will be overfilled? A company manufactures light bulbs. The lifetime for these bulbs is 4,000 hours with a standard deviation of 200 hrs. What lifetime should the company promote for these bulbs, whereby only! 2% burnout before the claimed lifetime? Hint: Consider learning what norm.ppfl) function does as a contrast to norm.cof() instead of guessing what integral limits will give an specified area. 5. The average life of a certain type of small motor is 10 years with a standard deviation of 2 years. The manufacturer replaces free all motors that fail while under guarantee. If she is willing to replace 3% of the motors that fail, how long a guarantee (in years) should she offer? You may assume that the lives of the batteries are normally distributed. Hint: Consider learning what norm.ppf function does as a contrast to norm.cof() instead of guessing what integral limits will give an specified area