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Restaurant marketing campaign

1. To help your restaurant marketing campaign target the right age levels, you want to find out if there is a statistically significant difference between the mean age of your customers and the age of the general population in your town: 43.1 years. A random sample of 50 of your customers shows a mean of 33.6 years and a standard deviation of 16.2 years. Test at a .05 level of significance.

2. Part of the assembly line will need adjusting if the consistency of the injected plastic becomes either viscous or not viscous enough as compared with a value (56.00) your engineers consider optimal. You will decide to adjust only if you are convinced that the system is "not in control"; that is, there is a real need for adjustment. The average viscosity for 13 recent measurements was 51.22 with a standard deviation of 3.18. Test at ? = .01.

3. Your Detroit division produced 135 defective parts out of the total production of 983 last week. The Kansas City division produced 104 defectives out of 1,085 produced in the same time period. Is the difference in defective rates between the two divisions statistically significant? Test at a .05 level.

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## Q : Expected value and variance of the random variable

What is the expected value and variance of the random variable X? Calculate the exact binomial probability.