# Stats Library

## Statistics Assignment Library

1. ##### A certain college gives aptitude tests in the sciences and the humanities to all entering freshmen.
A certain college gives aptitude tests in the sciences and the humanities to all entering freshmen. If X and Y are, respectively, the proportions of correct answers that a student gets on the tests in the two subjects, the joint...
2. ##### The average cost of an IRS Form 1040 tax filing at Thetis Tax Service is
The average cost of an IRS Form 1040 tax filing at Thetis Tax Service is \$157.00. Assuming a normal distribution, if 70 percent of the filings cost less than \$171.00, what is the standard deviation? Solution Let $X$ denote the...
3. ##### The distribution of the SAT scores in math for an incoming class of business students has a mean of 590 and Standard deviation
The distribution of the SAT scores in math for an incoming class of business students has a mean of 590 and Standard deviation of 22. Assume that the scores are normally distributed. a. Find the probability that an individual's SAT...
4. ##### The daily water consumption for an Ohio community is normally distributed with a mean consumption
The daily water consumption for an Ohio community is normally distributed with a mean consumption of 800,000 gallons and a standard deviation of 80,000 gallons. The community water system will experience a noticeable drop in water pressure when the daily...
5. ##### A cement truck delivers mixed cement to a large construction site. Let x represent the cycle time in minutes for the truck
A cement truck delivers mixed cement to a large construction site. Let x represent the cycle time in minutes for the truck to leave the construction site, go back to the cement plant, fill up, and return to the construction...
6. ##### In general, prove Bonferroni’s inequality
If $P(E) = 0.9$ and $P(F) = 0.9$, show that $P(EF) \geq 0.8$. In general, prove Bonferroni's inequality, namely that $P(EF) \geq P(E) + P(F)- 1$. Solution We know that $P(E \cup F)\leq 1$, because probabilities by definition are less...
7. ##### A psychologist has devised a stress test for dental patients sitting in the waiting rooms. According to this test
A psychologist has devised a stress test for dental patients sitting in the waiting rooms. According to this test, the stress scores (on a scale of 1 to 10) for patients waiting for root canal treatments are found to be...
8. ##### If electricity power failures occur according to a Poisson distribution with an average of 3 failures
If electricity power failures occur according to a Poisson distribution with an average of 3 failures every twenty weeks, calculate the probability that there will not be more than one failure during a particular week. Solution Let $X$ denote the...
9. ##### A consulting engineer receives on average 0.7 requests per week. Find the probability that
A consulting engineer receives on average 0.7 requests per week. Find the probability that a) In a given week, there will be at least one request; b) In a given 4 week period there will be at least 3 requests....
10. ##### The actual amount of coffee (in grams) in a 230-gram jar filled by a certain machine
The actual amount of coffee (in grams) in a 230-gram jar filled by a certain machine is a random variable whose probability density is given by  \begin{aligned} f(x)=\left\{ \begin{array}{ll} 0 & \hbox{$x \leq 227.5$;}\\ \frac{1}{5} , & \hbox{\$227.5 <...