Welcome to your assessment! Please read all instructions carefully. Write neatly, show all work (problems without adequate work will receive no credit), make sure answers are in the appropriate form, and double-check your work for accuracy. Good luck! 1. An electronic product contains 40 integrated circuits. The probability that any integrated circuit is defective is 0.01, and the integrated circuits are independent. The product operates only if there are no defective integrated circuits. a. (5 points) Does a binomial distribution apply to this scenario? Please explain. b. (5 points) What is the probability that the product operates?2. The number of views of a page on a Web site follows a Poisson distribution with a mean of 1.5 per minute. a. (5 points) What is the probability of two or fewer views in 10 minutes? b. (5 points) Does the answer to the previous part depend on whether the 10-minute period is an uninterrupted interval? Explain.2. The number of views of a page on a Web site follows a Poisson distribution with a mean of 1.5 per minute. a. (5 points) What is the probability of two or fewer views in 10 minutes? b. (5 points) Does the answer to the previous part depend on whether the 10-minute period is an uninterrupted interval? Explain.3. (5 points) An adult can lose or gain two pounds of water in the course of a day. Assume that the changes in water weight are uniformly distributed between minus two and plus two pounds in a day. What is the standard deviation of a person's weight over a day? 4. (5 points) The manufacturing of semiconductor chips produces 2% defective chips. Assume that the chips are independent and that a lot contains 1000 chips. Use the normal distribution to approximate the probability that between 20 and 30 chips are defective.3. (5 points) An adult can lose or gain two pounds of water in the course of a day. Assume that the changes in water weight are uniformly distributed between minus two and plus two pounds in a day. What is the standard deviation of a person's weight over a day? 4. (5 points) The manufacturing of semiconductor chips produces 2% defective chips. Assume that the chips are independent and that a lot contains 1000 chips. Use the normal distribution to approximate the probability that between 20 and 30 chips are defective.5. The demand for water use in Phoenix in 2003 hit a high of about 442 million gallons per day on June 27 (http://phoenix.gov/WATER/wtrfacts.html). Water use in the summer is normally distributed with a mean of 310 million gallons per day and a standard deviation of 45 million gallons per day. City reservoirs have a combined storage capacity of nearly 350 million gallons. a. (5 points) What is the probability that a day requires more water than is stored in city reservoirs? b. (5 points) What reservoir capacity is needed so that the probability that it is exceeded is 1%?5. The demand for water use in Phoenix in 2003 hit a high of about 442 million gallons per day on June 27 (http://phoenix.gov/WATER/wtrfacts.html). Water use in the summer is normally distributed with a mean of 310 million gallons per day and a standard deviation of 45 million gallons per day. City reservoirs have a combined storage capacity of nearly 350 million gallons. a. (5 points) What is the probability that a day requires more water than is stored in city reservoirs? b. (5 points) What reservoir capacity is needed so that the probability that it is exceeded is 1%?6. The life of automobile voltage regulators has an exponential distribution with a mean life of 6 years. You purchase a 6-year-old automobile with a working voltage regulator and plan to own it for 6 years. a. (5 points) What is the probability that the voltage regulator fails during your ownership? b. (5 points) If your regulator fails after you own the automobile 3 years and it is replaced, what is the mean time until the next failure?6. The life of automobile voltage regulators has an exponential distribution with a mean life of 6 years. You purchase a 6-year-old automobile with a working voltage regulator and plan to own it for 6 years. a. (5 points) What is the probability that the voltage regulator fails during your ownership? b. (5 points) If your regulator fails after you own the automobile 3 years and it is replaced, what is the mean time until the next failure