Statistics and Probability Answers

Powder milk is packed in 1-kilogram bag. An inspector from the Department of Trade and Industry (DTI) suspects that bags may not contain 1 kilogram. A sample of 40 bags produces a mean of 0.96 kilograms and a standard deviation of 0.12 kilogram. Is there enough evidence to conclude that the bags do not contain 1 kilogram as stated at 0.05 level of confidence?

A researcher claims that the monthly consumption of coffee per person is more than 19 cups. In a sample of 60 randomly selected people, the mean monthly consumption was 20. The standard deviation of the sample was 4 cups. Find the p-value of the test. On the basis of the p-value, is the researchers claim valid at 0.01 level of significance?

A certain kind of sheet metal has, on average, 3 defects per 19 square feet.

Assuming a Poisson distribution, find the probability that a 33 square foot metal sheet has at least 4 defects. Round your answer to four decimals.

If X is a R.V with PDF f(x) = x/6 when x = 1, 2, 3 and f(x) = 0, otherwise. Find E(X+2)²

Find the variance of the R.V. whose M.G.F is ((e^-t)/12) * (2 + e^t + 6e^3t + 3e^6t)

An apple juice producer buys apples from a large apple grove that has one variety of apple. The amount of juice squeezed from these apples is approximately normally distributed, with a mean of 4.70 ounces and a standard deviation of 0.40 ounce. Suppose that you select a sample of 25 apples

a) The probability is 70% that the sample mean amount of juice will be contained between what two values symmetrically distributed around the population mean?

b) The probability is 77% that the sample mean amount of juice will be greater than what value?

For a data set of the pulse rates for a sample of adult​ females, the lowest pulse rate is 36 beats per​ minute, the mean of the listed pulse rates is x=71.0 beats per​ minute, and their standard deviation is s=12.3 beats per minute.