BBBQT1224 Business Statistic 1 . Tutorial 5 Topic: Continuous Distribution (Normal Distribution + Inverse) The continuous random variable Z has a standard normal distribution, N(O,1). Find the following probabilities by using tables. a) P(X>2) b) P(0.74SZS 2) c) P(0.3 5 Z s 0.7) d) P(|Z| > 0.8) The random variable Z has a standard normal distribution. Find the value of a it a) P(Z > a) = 0.3621 b) P(Z > a) = 0.9666 c) P(a k) = 0.85 A medical expert has 100 potential new pain killers under clinical test. About 20% of all pain killers that reach this stage are eventually licensed for sale. What is the probability that at least 25 of the 100 pain killer are eventually licensed? Assume that the binomial assumptions are satisfied, and use a normal approximation with continuity correction. 5. A study was conducted in order to determine if any link existed between cellular phone usage and the development of brain cancer. Data from this study indicated that the monthly phone usage for all users is approximately normally distributed with mean 2.4 hours and standard deviation 1.1 hours. Up to how many hours does the lower 80% of the users spend on the phone? 6. Sixty two percent of 12th graders attend school in a particular urban school district. If a sample of 500 12th grade children is selected, find the probability that at least 280 are actually enrolled in school. 7. Use the normal approximation to the binomial to compute the probability of observing 460 or fewer in a sample of 1,000 residents from Scotland favoring consolidation if we assume that 50% of the entire population favors the change. 8. A really tough quiz has 50 multiplechoice questions, each with four possible answers. Use a normal approximation to calculate the probability of randomly guessing the correct answers for 12 to 20 (inclusive) of the questions. 9. A study was conducted in order to determine if any link existed between cellular phone usage and the development of brain cancer. Data from this study indicated that the monthly phone usage for all users is approximately normally distributed with mean 2.4 hours and standard deviation 1.1 hours. Up to how many hours does the lower 80% of the users spend on the phone? a. 1.82 hours b. 3.33 hours 0. 1.47 hours 01. 3.12 hours e. 3.81 hours