3334

Statistics Confidence Interval Level: High School

The probability is 1 in 4,000,000 that a single auto trip in the United States will result in fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probility of a fatal accident over a lifetime?

Explain your reasoning carefully. Hint: Assume independent events. Why might the assumption of independence be violated?

(b) Why might a driver be tempted not to use a seat belt "just on this trip"?

3333

Statistics Confidence Interval Level: High School

A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that

(a) both will fail?

(b)Neither will fail?

(c) One or the other will fail? Show all steps carefully

3332

Statistics Confidence Interval Level: High School

Why is population shape of concern when estimating a mean? What does sample size have to do with it?

3331

Statistics Confidence Interval Level: High School

State the main points of the Central Limit Theorem for a mean.

3317

Statistics Confidence Interval Level: High School

In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive.

(a) Construct a 95 percent confidence interval for the population proportion of positive drug tests.

(b) Why is thenormality assumption not a problem, despite the very small value of p? (Data are from Flying 120, no. 11 [November 1993], p. 31.)

3316

Statistics Confidence Interval Level: High School

A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were 3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477

(a) Construct a 90 percent confidence interval for the true mean weight.

(b) What sample size would be necessary to estimate the true weight with an error of ± 0.03 grams with 90 percent confidence?

(c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture. (Data are from a project by MBA student Henry Scussel.)

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