<p> Sr. 4 Applied Math 40S “lights and tires”</p><p>This assignment is out of 12 marks. When answering applied math questions the process of finding the answer is of great importance. Always be sure to explain how you got your answer. This may include showing all your work or briefly explaining your answer in sentences. </p><p>This question must be done on graph paper, in pencil and with a ruler.</p><p>Essential skills -Solving normal distribution probability questions -Drawing normal distribution probability questions -Given probability, solve for discrete data</p><p>For each question below:</p><p>Draw a normal curve for each situation. Answer the question. </p><p>1 The “life” of a standard light bulb is normally distributed with a mean of 3000 hours and a standard deviation of 52 hours. If the porch light at a house is set to be on for 8 hours each evening, what is the probability that the light does not have to be replaced before a year is over? (3 marks) 2 A tire manufacturer states the mean pressure in the tires should be 32 pounds per square inch. The standard deviation of pressure is 1.6 pounds per square inch. The manufacturer also states that unicycle tires with pressure less than 27 or more than 36 pounds per square inch could be unsafe to ride. If the air pressure in unicycle tires is normally distributed, how many unicycles out of 1000 are unsafe due to the air pressure in the tires? (3 marks)</p><p>3 A machine dispenses coffee into paper cups. The cups will hold 7.2 ounces. The mean of the machine is set to dispense 7 ounces of coffee. The standard deviation is 0.95 ounces. What is the probability the cup will overflow.</p><p>(2 marks)</p><p>4 The “life” of a Megacell battery is normally distributed. They have a mean life of 70 hours and a standard deviation of 7.2 hours. The battery is Jake’s MP3 player lasted longer than 70% of all batteries he had ever used before it died. How long did it last?</p><p>(2 marks)</p><p>5 The mean weight of the African Goldfish is normally distributed with a weight of 2300 grams and a standard deviation of 150 grams. Sandy has an African Goldfish that weighs less than 10% of all fish. How much does it weigh?</p><p>(2 marks)</p>