MDM4U (SOLVING PROBLEMS WITH THE NORMAL DISTRIBUTION)

Assignment 18: Solving Problems with the Normal Distribution 1. A potato chip company creates bags of chips with a mean weight of 144.5 grams and a standard deviation of 7.6 grams. The company will not allow any bag weighing less than 130 grams or more than 160 grams to be sold. What percentage of bags will be sold? 2. Karen's albums have a mean number of songs of 13.1 with a standard deviation of 1.2 songs. If Karen sets her music player to shuffle albums, what is the probability that it will select an album that has exactly 12 songs? 3. A manufacturer of magic markers has 2800 markers randomly chosen from a production line and tested for toxic scents. A marker has a 94% chance of having a nontoxic scent. Use the normal approximation, if possible, to determine the probability there will be more than 150 toxic-smelling markers. 4. A job interview requires a standardized test to be written. Last year, the mean score for the test was 65 with a standard deviation of 7.2. Only those applicants scoring in the top 20% were eligible for a call-back interview. What score would someone need on the test in order to receive a call-back interview? 5. Calculate the probability that 500 rolls of two regular 8-sided dice will include more than 50 sums of 7. 6. A computer security expert is investigating a particularly dangerous strain of malware. She determines that the malware has approximately a 42% chance of infecting a typical computer setup. Her company knows that 30 of its computers were exposed to the malware. a. If possible, using a normal approximation of the binomial distribution, find the probability that: 1. none of the computers were infected; 2. all of the computers were infected; 3. exactly 10 computers were infected; 4. more than 20 computers were infected. b. The expert makes $40/h. She estimates it will take her approximately 4.5 hours to remove the malware from infected computers. Based on your calculations above, how much money should the company budget for fixing these computers