2. Suppose X is a normally distributed random variable with a mean of 50 and a standard deviation of 2. Find the associated X-value for each of the following z-scores a. z = 1.28 b. z = 5.66 C. 230 d. z = -1.56 3. Manufacturing all over the world is faced with what to do with hazardous waste materials . The concentration of blood toxins found in captured frogs near a particular manufacturing plant were found to follow a normal distribution with a mean of 0.08 % and a standard deviation of 0.005 %. Frogs with toxin levels in the top 10% are automatically retested in case the extreme result was due to measurement error . What toxin levels will result in an automatic retesting ? The mileage ratings (in miles per gallon ) of hybrid vehicles on the market today follow a normal distribution with a mean of 42.5 miles per gallon (mpg ) and a standard deviation of 9.3 mpg . Owners of hybrid vehicles whose mileage rating is in the top 12 % of mileage ratings automatically qualify for a tax exemption of their vehicle registration fees What is the minimum mileage rating needed to qualify for this tax exemption ? 5. Weights of newborn babies born in urban hospitals in the United States are normally distributed with a mean of 3420 grams and a standard d deviation of 495 grams . Any newborn in the 10th percentile or less of body weight is automatically put in the neonatal intensive care unit (NICU ) for at least 3 days and is given a strict dosage of nutrients Babies with what body weight are automatically sent to the NICU at urban hospitals ? 6. Credit card usage is requiring an increasing amount of information from users in order to avoid credit card theft and abuse . For example , an applicant 's annual income , among other factors , will dictate their credit limit . It is know that the annual income of last year's American Express Platinum Card applicants in the San Francisco Bay Area follow a normal distribution with a mean of $87,000 and a standard deviation of $10,000 . American Express automatically approves Platinum Card applicants whose salary is in the top 15 % of all applicants . What is the minimum income required to be automatically approved for a Platinum Card ? 7. Suppose you record how long it takes you to get to school over many months and discover that the one -way travel times , in minute s, are approximately normally distributed with a mean of 13.88 minutes and standard deviation of 4 minutes . If your first class is at 10:30 am, what is the latest time you should leave everyday so that you are on time at least 93.7 % of the time ? 8. Flat screen monitors manufactured by an offshore OEM supplier have life spans which are normally distributed with a mean life of 13,500 hours and a standard deviation of 1,200 hours . Suppose that you are a large buyer of these monitors for your company , which you subsequently sell on the open market , and your company wants to guarantee these monitors for a minimum life span . What should you set the minimum life span to be, if you want no more than 3% of your sales to result in having to provide the customers with new monitors to replace failed ones ? How many days of consecutive usage would you be guaranteeing to your customers ? 9. A statistics instructor has decided to give the top 15 % of all students in her class A's based on total points in the course . Suppos e that the total points in the course have a mean of 750 with a standard deviation of 85 and the total points are approximately normally distributed . What number of total points will provide a student an A in the course