Exam 12: Sampling Distributions

The distribution of total body protein in adult men with liver cirrhosis is approximately Normal, with mean 9.8 kg and standard deviation 0.1 kg. If you take a random sample of 25 adult men with liver cirrhosis, what is the probability that their average total body protein is between 9.75 and 9.85 kg?

As many as 20% of all Americans contract influenza each year. A sample of 400 randomly selected Americans is chosen and the number with influenza is recorded. Let X represent the number with influenza in the sample. If X = 75 individuals are found to have influenza, what is the standard deviation of the sampling distribution?

The World Health Organization recorded a total of 148 cases of parasitic Guinea worm infection worldwide in 2013, down from millions of cases just two decades ago. The sharp decline in infections is attributed primarily to water filtration using a simple cloth. A research paper found that, in 10 replications, a polyester cloth filtered 100% of the organisms carrying the Guinea worm larvae. Which of the following is correct about the numerical summaries 148 and 100%?

A large school district in southern California asked all of its eighth-graders to measure the length of their right foot at the beginning of the school year, as part of a science project. The data show that foot length is approximately Normally distributed, with a mean of 23.4 cm and a standard deviation of 1.7 cm. Suppose that 25 eighth-graders from this population are randomly selected. Approximately what is probability that the sample mean foot length is less than 23 cm?

The World Health Organization estimates that 5% of all adults in sub-Saharan Africa are living with HIV/AIDS. A survey takes a random sample of 1600 adults from all over sub-Saharan Africa and finds that 84 have HIV/AIDS. What is the probability that a random sample of 1600 adults in sub-Saharan Africa would have less than 4.5% living with HIV/AIDS?

The distribution of vitamin C amount in the vitamin drops produced by a given factory is approximately Normal, with a mean of 60.0 mg and a standard deviation of 0.5 mg. If you take a random sample of 25 vitamin drops, what is, approximately, the probability that the average vitamin content x̄ is between 60.25 and 60.75 mg?

The distribution of total body protein in healthy adult men is approximately Normal, with mean 12.3 kg and standard deviation 0.1 kg. If you take a random sample of 25 healthy adult men, what is the probability that their average total body protein is between 12.25 and 12.35 kg?

You should not use the Normal approximation to the distribution of p̂ when the sample size N is small.