MDM4U f1+ B - Normal Distriubtion Assignment Answer all questions with full solutions. Make sure your work is legible, even after you have scanned it, and submit it as a single file. 1. Look at the sketches of continuous probability distributions below. a. b. c. For each sketch, give an example of a situation which might give rise to such a probability distribution, fully explaining your reasoning. (6 marks) 2. In many situations, the normal distribution can be used to approximate the binomial distribution. a. Explain the conditions in which this can be done, and explain why we might want to take advantage of this property. b. Give an example of a situation in which we could do this. c. Give an example of a situation in which we would not be able to make this approximation and explain why. (6 Marks) 3. A species of alien has a mean height of 23 cm and a standard deviation of 3.6 cm. What is the probability that an alien chosen at random has a height of more than 20cm? (6 Marks) 4. Researchers have observed that regular smokers have an average lifespan that is normally distributed and is 68 years with a standard deviation of 10 years. What percent of smokers will live beyond age 76? (4 Marks) GO TO: THE DROPBOX AND UPLOAD YOUR WORK. 5. The life span of a particular species of turtle are normally distributed with a mean of 180 years and a standard deviation of 40 years. What is the probability that one of these turtles will live more than a century? (4 Marks) 6. A second species of alien has a mean height of 71 cm and a standard deviation of 5.3 cm. An alientologist discovers that 30% of them bump their heads getting into their spaceship. What is the height of the spaceship door? (6 Marks) 7. In Bayfield, 65% of residents read the Bayfield Breeze, a local online blog. Dennis wants to know what people think of the blog, so he stops 40 people on the street to ask them if they read it. a. Verify that the normal distribution can be used to approximate this situation. b. What is the mean and standard deviation of the number of people he finds that read the Breeze? c. What is the probability that at least 25 of the people he asks read the blog? (9 Marks) 8. Yuen Zhi is running a ring toss event at a school fair. There is a 15% chance that each attempt wins a prize. She has 45 prizes and believes 250 people attempt the event. She is worried she won't have enough prizes. Can you reassure her she will probably be ok? (9 Marks) 9. We have been using the normal distribution to approximate situations that are in fact binomial events. a. Demonstrate how accurate the approximation is by using both approaches to find the probability of the same event. b. Describe the conditions under which the normal would give a less accurate approximation. c. Explain a situation in which the criteria for using the approximation would be met, ie. np 5 and n(1 p) 5, and yet you would decide not to use the normal distribution. (10 Marks) GO TO: THE DROPBOX AND UPLOAD YOUR WORK