Statistics and Probability Answers

An investigator wants to estimate the mean number of days since the onset of diabetes in diabetic patients. The investigator wants to be 95% confident that the sample estimate will be within 7 days of the true mean. The standard deviation is known to be 70 days. What sample size would be required?

16.24 College degrees. At the Statistics Canada Web site, www.statcan.gc.ca, you can find the percent of adults in each province or territory who have at least a university certificate, diploma, or degree at bachelor’s level or above. It makes no sense to find for these data and use it to get a confidence interval for the mean percent μ in all 13 provinces or territories. Why not?

16.12 Number skills of young men. Suppose that scores on the mathematics part of the National Assessment of Educational Progress (NAEP) test for high school seniors follow a Normal distribution with standard deviation σ = 30. You want to estimate the mean score within ±10 with 90% confidence. How large an SRS of scores must you choose?

16.22 Sampling at the mall. A market researcher chooses at random from women entering a large suburban shopping mall. One outcome of the study is a 95% confidence interval for the mean of “the highest price you would pay for a pair of jeans.”
(a) Explain why this confidence interval does not give useful information about the population of all women
(b) Explain why it may give useful information about the population of women who shop at large suburban malls.

4. For the previous problem 51152, The sample of 100 screws turns out to have mean = 15.005mm. (Still testing against = 15 mm and assuming population standard deviation is known to be 0.04mm.) Does this give evidence that the lengths of the screws are longer than 15mm? Explain using the important values you use to make your decision.

2. A screw manufacturer makes specialized tiny screws that are 15mm long. The manufacturing process does not make every screw exactly 15mm long. If the lengths of the screws are normally distributed with population mean 15mm and population standard deviation 0.04mm. To test for quality control, 100 screws are to be measured. What is the distribution of the sample means for samples of size 100?

3. A screw manufacturer makes specialized tiny screws that are suppose to be 15mm long. The manufacturing process does not make every screw exactly 15mm long. The lengths of the screws are normally distributed with population standard deviation 0.04mm. A quality control manager thinks that the screws being made actually have mean lengths longer than 15mm. What is her null hypothesis and alternative hypothesis for testing this belief?

The variance of a given distribution is 25. What is the standard deviation.

The records show that 8% of the items produced by a machine do not meet the specifications. You take a sample of 100 units.

a. Find the expected value.
b. Find the standard deviation.

The time it takes to hand carve a guitar neck is uniformly distributed between 110 and 190 minutes.

a. Compute the variance.

3. Aquinas students were asked how many pizzas they have eaten in the last 10 days. Let the random variable X be the number of of pizzas a student has eaten in the last 10 days. Picking a student at random, we have the following probabilities:
Number of Pizzas
# of Pizzas 0 1 2 3 4 or more
P(x) 0.10 0.17 0.41 0.18 0.14

Find P(X>2)


4. Aquinas students were asked how many pizzas they have eaten in the last 10 days. Let the random variable X be the number of of pizzas a student has eaten in the last 10 days. Picking a student at random, we have the following probabilities:
Number of Pizzas
# of Pizzas 0 1 2 3 4 or more
P(X) 0.10 0.17 0.41 0.18 0.14


Find P(X<2)


5. A screw manufacturer makes specialized tiny screws that are 15mm long. The manufacturing process does not make every screw exactly 15mm long. Suppose we know that the lengths of the screws have population mean 15mm and population standard deviation 0.04mm. To test for quality control, 100 screws are to be measured. What is the distribution of

In San Francisco, 30% of workers take public transportation daily (Use binomial distribution)

1. In a sample of 10 workers, what is the probability that exactly three workers take public transportation daily (4 decimal places)

2. In a sample of 10 workers, what is the probability that at least three workers take public transportation daily (4 decimal places)

3. How many workers are expected to take public transportation daily? (2 decimal places)

4. Compute the variance of the number of workers that will take the public transport daily. (2 decimal places)

5. Compute the standard deviation of the number of workers that will take the public transportation daily. (3 decimal places)