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If two events are mutually exclusive, then the union of those two events is the sum of the individual probabilities of these two events.
A large statistics class took an exam. The scores followed a normal curve with mean 78 and standard deviation 10. Students who scored 90 or above got an A on the exam. Those who scored between 80 a
Scores on IQ tests have a symmetric distribution that is roughly bell-shaped. Reported IQs are scaled so that the distribution has a mean of 100 and a standard deviation of 15. Suppose that a standa
Find the probability that in a given year A exactly one major hurricane will strike the mainland, B at most one hurricane will strike the mainland, C mor than one major hurricane will strike mainlan
Consider a guessing game, where a number between 2 and 12 is chosen by rolling two dice. Try to find the best strategy for a player to guess the number.
Recently, the use of mammograms to screen for breast cancer was in the news. Let's suppose that 1% of women aged 30 - 40 have breast cancer and that a mammogram detects 90% of all cancers.
The scores on the Wechsler Adult Intelligence Scale are approximately Normal with \mu = 100 and \sigma = 15. What is the proportion of adults with scores between 90 and 110?
Scores on a university exam are Normally distributed with a mean of 68 and a standard deviation of 9. Using the 68-95-99.7 rule, what percentage of students score above 77?
From the probability distribution, find the mean and standard deviation for the random variable x, which represents the number of cars per household in a town of 1000 households.
The nine brand B cars that were tested averaged 32.1 mpg, and the standard deviation was 4.3 mpg. At =0.01, should it conclude that brand A cars have lower average gas mileage than do brand B cars?
Assume the heights of women normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. The U.S. Army requires that the heights of women between 58 and 80 inches. If a wo
Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $31,000 and a standard deviation of $3000. If 100 teachers are randomly selected,
In a recent study of 71 eighth graders, the mean number of hours per week that they watched television was 18.7 with a standard deviation of 5.8 hours. Find the 99% confidence interval.
Construct a 98% confidence interval for the population mean, M. Assume the population has a normal distribution. A random sample of 20 college students has mean annual earnings of $3480 with a stand
A survey of 600 non-fatal accidents showed that 166 involved the use of a cell phone. Construct a 99% confidence interval for the proportion of fatal accidents that involved the use of a cell phone.
We determined the sodium content of 15 boxes of corn flakes 300 grams. The data (in milligrams) are: 128.77, 131.15, 129.65, 132.33, 130.54, 130.72, 131.67, 133.02, 127.98, 130.12, 129.37, 129.91, 1
The Ohio Department of Agriculture tested 203 fuel samples across the state in 1999 for accuracy of the reported octane level. For premium grade, 14 out of 105 samples failed (they didn't meet ASTM
The true weight of "10-pound" sacks of potatoes processed at a certain packaging house follows a normal distribution with mean of 10.1 pounds and standard deviation of 0.2 pounds.
Exposure of certain fruit fly population to an insecticide has produced 2 kinds of mutations: 20% have wing mutations, 15% have an eye mutation and 5% have both. A fly is selected at random. If the
If 20% of all seams need reqorking, what is the probability that rivets is defective? How small should the probability of a defective be to ensure that only 10% of all seams need reworking?
When do we use Chevbychev's theorem? with what kinds of problems? and for what purpose? please explain clearly for lifesaver.
Please explain both Poisson and exponential distributions and the difference between them. Please include extensive details for lifesaver.
A post office has two counters where customers can buy stamps, etc. If you are interested in the number of customers in the two queues that will form for the counters, what would you take as sample