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There were 42 different presidents of the United States from 1789 through 2000. What is the probability that at least two of them had the same birthday?
Two balls are selected randomly from urn containing 8 yellow, 4 black, and 2 red balls. Let Y represent the number of black balls chosen. The discrete probability distribution is shown below.
An automotive manufacturer has chosen 10 car seats to study the Rockwell hardness of seat recliner mechanism. A sample of 8 has an average of 44.795 and standard deviation of 0.402. At 95% percent
In current Austin marathon, the distribution of finishing times for the female runners who completed the race were approximately normally distributed with a mean of 280 minutes and a standard deviat
Make a list of all samples of size 2 that can be drawn from this set of integers. [Sample with replacement; that is, the first number is drawn, observed, and then replaced (returned to the sample se
In a large metropolitan area, past records revealed that 45% of all the high school graduates go to college. each sttudent's choice to go to college is independent. From 50 graduates selected at ran
Gizmo and Co. is major player in nationwide market for Gizmos. They manufacture 14,000 Gizmos every year. Their number of defects per year is normally distributed with mean 3,000 units and standard
If the true average life of the light bulbs is really 1,965 hours with standard deviation 150 hours, what is the probability that the mean of a random sample of n=100 measurements would exceed 2,000
Determine the approximate shape of the distribution of the sample means(uniform, normal, skewed, other)? What value do the sample means tagert?
Researchers have discovered a new genetic marker for a form of cancer. Ten percent of the overall population carry this marker, and of all the people who develop this cancer, 33% carry the marker.
Conceptually, why does it make sense that the t critical values are always as large or larger than z critical values for the same level of confidence?
A venture capital company feels that rate of return (X) on proposed investment is approximately normally distributed with mean 30% and standard deviation 10%.
Discuss the difference between mutually exclusive and independent events.
A group of n people of different heights are randomly ordered. Given that the very shortest person is first and the very tallest person is last, what is the probability the intermediate one are orde
The tool shop has 8 power screw drivers and two have a short. A foreman takes 4 of screw drivers to his crew. That is the probability that fewer than two have a short?
Throughout an 80 hour period, there are 7 unplanned work stoppages on production line. Determine the rate per hour at which stoppages occur.
In a sample of 112 washers, 8 are "our of spec". Estimate the proportion of washers that are being prodiced tat are out of spec.
Assume the length of time students take in writing a standard entrance examination is normally distributed with mean 60 minutes, std. deviation 8 minutes
A biologist weighs 7 lab mice. The following results were obtained: 31.2, 28.3, 32.8, 29.1, 24.0, 38.2, 33.4 g. Find a 99% confidence interval for the mean weight. Show work
You're flipping a fair coin. Initially you just flip it. After that, if it was heads previous round you turn it over to tails (so it guarantees a tails in the current round), and if it was tails you
A mammologist gathered 90 female kangaroo rats and 27 of them were pregnant. Employ the normal distribution to find a 95% confidence interval for the pregnancy rate in female kangaroo rats. Show wor
Sickle-cell anemia is hereditary medical condition affecting red blood cells that is thought to protect against malaria, a debilitating parasitic infection of the liver and blood.
A building may fail by excessive settlement of foundation or by collapse of the superstructure. Over the life of the building, the probability of excessive settlement of the foundation is estimated
Assume 6 people check their coats in checkroom. If all claim checks are lost and 6 coats are randomly returned, determine the probability that all the people will get their own coats back?