Question:

A random sample of 40 Americans yielded a sample mean of 67 gallons of carbonated beverages per year. Assume that the population standard deviation is 22 gallons per year, and the consumption of carbonated beverages per year follows a normal distribution. List and check the conditions, calculate a 95% confidence interval, and write it in a complete sentence related to the scenario.

The University of Greatlake Surveys of Consumers found that the mean index of consumer sentiment for December 2015 was 82.9. Suppose the population is normal and this result was based on a random sample of size 85, which had a standard deviation of 12. List and check the conditions, construct a 95% confidence interval for the population mean consumer sentiment, and write it in a complete sentence related to the scenario.

A survey of customers at a local supermarket asks whether they found shopping at this market more pleasing than at a nearby store. Of the 3000 forms distributed to customers, 429 were filled in and 276 of these said that the experience was more pleasing. With 90% confidence, list and check the conditions, calculate the confidence interval to estimate the true proportion of customers that consider this market more pleasing than the other store, and write it in a complete sentence related to the scenario.

The service department at a new car dealer checks for small dents in cars brought in for scheduled maintenance. It finds that 27 of 86 randomly-sampled cars have a dent that can be removed easily. The service department wants to estimate the percentage of all cars with these easily repaired dents. List and check the conditions, construct a plus-four confidence interval to estimate the percentage with 99% confidence, and write it in a complete sentence related to the scenario.

A political candidate is anxious about the outcome of the next election. To have his next survey result produce a 95% confidence interval with margin of error of no more than 0.03, how many eligible voters are needed in the sample?

(1 point) The following function is called a Gaussian Function. Gaussian functions are used in statistics, image processing, signal processing, and in mathematics to solve heat and diffusion equations. (x-6)2 f(x) = ae 22 Find the first and second derivative of the given Gaussian function when a = 3, b = 1, and c = 2 f' (x ) = f" (x) = NOTE: It will be much easier to type your answer if you simplify the derivative functions (but is not necessary).Problem 3 (30 points) A car wash has one stall in which customers can clean and wax their cars, and room to accommodate one additional car when the stall is occupied. Cars arrive at the station for gasoline according to a Poisson process, at a mean rate of 5 per hour. The time required for service a car appears to be exponentially distributed, with a mean of 20 minutes. Determine: a. The average number of cars simultaneously at the station. (10 points) b. The time a customer is expected to wait in the car wash (10 points) c. The average rate at which customers are denied entrance to the car wash (10 points)