1. A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and a standard deviation of 0.2 ounce. If a sample of 9 cups is selected, find the probability that the mean of the sample will be greater than 12.1 ounces?

2. A student answers all 48 questions on a multiple-choice test by guessing. Each question has four possible answers, only one of which is correct. Find the probability that the student gets exactly 15 correct answers. Use the normal distributions to approximate the binomial distribution.

2. Originally Posted by loutja35
1. A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and a standard deviation of 0.2 ounce. If a sample of 9 cups is selected, find the probability that the mean of the sample will be greater than 12.1 ounces?

2. A student answers all 48 questions on a multiple-choice test by guessing. Each question has four possible answers, only one of which is correct. Find the probability that the student gets exactly 15 correct answers. Use the normal distributions to approximate the binomial distribution.
1. You should know that the sample mean $\displaystyle \overline{X}$ follows a normal distribution with mean 12 and standard deviation $\displaystyle \frac{0.2}{\sqrt{9}}$. Use this to calculate $\displaystyle \Pr(\overline{X} > 12.1)$ (see my reply at another of your posts for how to do this sort of calculation).

2. mean = np = .... and variance = np(1 - p) = .... This is simply substituting into a formula (which will be in your class notes or textbook. Have you read them?) and doing the calculation. What have you done and where do you get stuck?