Use Continuous Probability, Data management 12

1. Which of the following has a negatively skewed distribution? a. failure rates for a model of computer printer during its rst four years of use b. the numbers of children in Canadian families 0. adult shoe sizes d. waiting times between customers arriving at a pizza outlet during lunchtime 2. Which of the following describes the normal distribution? a. bimodal c. asymmetrical b. skewed d. unimodal 3. If a set of data has a mean of 12 and a standard deviation of 3, what is the z-score for a value of 9? a. l b. l c. i] d. 0 4. Predictions based on a sample taken from a normally distributed population are most reliable when a. the sample size is small b. the sample size is large 0. the standard deviation is small d. the standard deviation is large 5. For which of the binomial distributions listed below is the normal distribution not a reasonable approximation? a. n=50,p=0.4 b. n=40,p=0.12 c. n=75,p=0.ll d. n=40,p=0.8 6. Assuming that a normal distribution is a reasonable approximation for a binomial distribution, what value is used to approximate the standard deviation? a. npq b. up 0. npq d. imp Short Answer and Problems (30 marks): 7. In the space below, sketch the graph of a distribution that is positively skewed, one that is negatively skewed and one that is bimodal. Be sure to identify which is which. Provide an example for each distribution. (3 marks) 8. 10. ll. 12. 13. In the space below, sketch the normal distribution curve characterized by a mean of 9 and a standard deviation of 1.7. Indicate the areas under the curve that correspond with the Empirical Rule and fully label the graph. ( 3 marks) A company produces boxes of candy that contain a mean of 50 candies each. The standard deviation is 2. Quality control will reject any box with fewer than 48 candies. a) What is the probability that a box selected at random contains exactly 51 pieces? (3 marks) b) What percentage of the boxes will quality control reject as containing too few candies? ( 3 marks) QuenCola, a soft-drink company, knows that it has a 42% market share in one region of the province. QuenCola's marketing department conducts a blind taste test with 100 people at a mall in the region. Use a normal approximation to calculate the probability that exactly 40 of these people will choose QuenCola. ( 5 marks) Suppose the commuting time from North Bay to Barrie varies uniformly from 135 min to 180 min, What is the probability that the drive will take less than 160 min? Illustrate with a graph. ( 3 marks) The life spans of a particular species of turtle are normally distributed with a mean of 180 years and a standard deviation of 40 years. What proportion of these turtles will live between 100 and 260 years? ( 6 marks) It is estimated that 10% of the vehicles entering Canada from the United States carry undeclared goods. Use the normal approximation to calculate the probability that a search of 500 randomly selected vehicles will nd more than 60 with undeclared goods. (4 marks)