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 <...