Probability and Statistics
Complete each problem using z scores and the table on page 591 - 594 in the textbook. Use the TI 83 calculator to check your results.
Voter registration records show that 68% of all voters in Indianapolis are registered as Republicans. If you use a random number dialing device to contact 150 residential telephones in Indianapolis for a political poll, what is the probability that 63% or less respond that they are registered Republicans?
Suppose that 47% of all adult men think that they do not get enough time for themselves. An opinion poll interviews 1025 randomly chosen men and records the proportion who feel they don't get enough time for themselves. What is the probability that the poll gets a sample in which more than 50% say they do not get enough time for themselves?
The Harvard College Alcohol Study interviewed a simple random sample of 14,941 college students about their drinking habits. Suppose that half of all college students "drink to get drunk" at least once in a while. That is, p=0.5.
What are the mean and standard deviation of the proportion p ^ of the sample who drink to get drunk.
What is the probability that p ^, the sample proportion, is between 0.49 and 0.51.
The level of nitrogen oxides (NOX) in the exhaust of a particular model varies normally with mean 0.2 grams per mile (g/mi) and standard deviation 0.05 g/mi. Government regulations call for NOX emissions to be no higher than 0.3 g/mi.
What is the probability that a single car of this model fails to meet the NOX requirement?
A company has 25 cars of this model in its fleet. What is the probability that the average NOX level x ¯ of these cars is above the 0.3 g/mi limit?
The Wechsler Adult Intelligence Scale (WAIS) is a common "IQ test" for adults. The distribution of the WAIS scores for persons over 16 years of age is approximately normal with mean 100 and standard deviation 15.
What is the probability that a randomly chosen individual has a WAIS score of 105 or higher?
What are the mean and standard deviation of the sampling distribution for the average WAIS score x ¯ for a simple random sample of 60 people?
What is the probability that the average WAIS score of the simple random sample of 60 people is 105 or higher?