BAD 2323 Ch6 Hwk Normal Probability Distribution 1. If a normal distribution has a mean of 600 and a standard deviation of 100: a. What is the probability of finding a value above 650? b. What is the probability of finding a value above 400? c. What is the probability of finding a value less than 550? d. What is the probability of finding a value between 625 and 645? e. What is the probability of finding a value less than 800? 2. A production process is supposed to have only a 2% defect rate. A sample of 900 items is taken and 30 items are found to be defective. Calculate the following: a. the mean b. the standard deviation c. the probability of having 30 or more defects d. Is the machine working properly? 3. A normal distribution of grades has a mean of 75 and standard deviation of 6. a. If the top 20% should get an "A", what should be the lowest "A"? b. If the bottom 15% should get an "F", what should be the highest "F"? 4. A sample of 800 is taken from a large population having 1% defective. The normal distribution is an approximation of the binomial. a. Find the probability of at least 11 defectives. b. Find the probability of no more than 11 defectives. c. Find the probability of exactly 11 defectives. 5. In a normal population the defect rate is 10%. A sample of 100 is taken. The normal is an approximation of the binomial. a. What is the probability of finding no more than 5 defectives? a. What is the probability of finding more than 5 defectives? c. What is the probability of finding exactly 5 defectives? 6. In a normal population 5% of items are defective. A sample of 1,000 items is examined. The normal is an approximation of the binomial. a. Calculate the probability of finding more than 60 defectives. b. Calculate the probability of finding fewer than 60 defectives. 7. In a normal population 6% of items are defective. A sample of 100 items is examined. The normal is an approximation of the binomial. a. Calculate the probability of finding more than 4 defectives. b. Calculate the probability of finding fewer than 4 defectives. c. Calculate the probability of finding exactly 4 defectives. 8. The normal is an approximation of the binomial. In a normal population with n = 250 and p = .10 calculate: a. P( 20 <= r <= 35) b. P( r => 18) c. P( r <= 22) d. P( r <= 35) 9. A production process has a defect rate of 2%. A sample of 500 items is taken. If the normal is an approximation of the binomial, then calculate: a. the average number of defectives you would expect to find in the sample, ( the sample mean of defectives) b. the standard deviation of the distribution c. the probability of finding between 7 and 13 defectives in the sample. 10. A task never takes below 10 minutes or above 20 minutes. This is a uniform distribution. Calculate the range Calculate the mean Calculate the variance Calculate the probability that a task will take no more than 12 minutes P( x <=12) Calculate the probability that a task will take at least 12 minutes P ( x => 12) Calculate the probability that a task will take no more than 17 minutes P ( x <= 17) Calculate the probability that a task will take will take between 12 and18 minutes