Which of the following families is characterized by having n…

Questions

Which оf the fоllоwing fаmilies is chаrаcterized by having numerous stamens and many pistils?

(12 pоints) Indicаte whether eаch stаtement is true оr false. Briefly justify yоur answer using an example or concepts discussed in class. Suppose we pick a random business in Santa Clara right now.  Let be the event the business is currently open. Then the event  and its complement, are mutually exclusive. Suppose on Friday the weatherman says that there is a 50% chance of rain for Saturday and a 50% chance of rain on Sunday. This means that there is a 100% chance it will rain sometime this weekend. (12 points) Of all college students who are eligible to give blood, about 18% do so on a regular basis. Each month a local blood bank sends an appeal to give blood to 250 randomly selected students. Check the conditions that this experiment satisfies the criteria for a Binomial Probability Experiment. Calculate the mean (expected value) and standard deviation of the number of students that will donate blood in a given month. Would it be unusual for 60 students to donate blood in the month of November? (18 points) Happy Treads tire company has a line of automotive tires. The useful life of these tires is normally distributed with mean 57,500 miles and standard deviation 2350 miles. Find the probability that a randomly selected tire lasts between 52000 and 55000. Happy Treads is considering offering a 54000-mile warranty with a full replacement guarantee for tires that wear out before 54000 miles. What is the probability that a randomly selected tire will need to be replaced under the guarantee. The guarantee is too generous. Happy Treads wants to revise it so that they will only need to cover the tires with the shortest 2% of life spans. How long should the guarantee be for? (16 points) An insurance company knows that in the entire population of millions of apartment owners, the mean annual loss from damage is $90 and the standard deviation of the losses is $475.  The population distribution of losses is strongly right skewed: most policies have $0 loss, but a few have large losses.  If the company considers its 10,000 policy holders as a simple random sample from this population, this sample will be large enough for the central limit theorem to apply. Determine the expected value and standard error of mean loss among the sample of 10,000 policy holders. Check that the conditions for the central limit theorem apply. Find the probability that the insurance companies 10,000 policy holders experience a mean loss less than $83. Find the probability that the insurance companies 10,000 policy holders experience a mean loss of between 91 and 103. (12 points) Suppose that 37% of all college students would rent textbooks if that option were available to them. If a polling group chose a simple random sample of 1279 students from the population.  Find the sampling distribution for the proportion of the sample would rent textbooks if that option were available Find the probability that the percentage of students in the sample who would rent textbooks is between 35% and 38%. (12 points) In a random sample of 12,447 hip replacement or revision surgery procedures nationwide, 162 patients developed a surgical site infection. Construct a 98% confidence interval for the proportion of surgeries that will experience surgical site infection. Be sure to give the estimated standard error and the margin of error before stating the upper and lower limit of the interval. Based on your interval, would it be plausible to say that 2% of hip replacement or revision surgeries will result in surgical site infection? Briefly explain. (12 points) A market research company surveyed 55 people, asking how much money they spent on their child’s last birthday gift. The sample distribution was roughly bell shaped with a mean of $39.25 and a standard deviation of $10.05. These results yielded a 95% confidence interval for the average amount parents spend on their child’s birthday gifts of between $36.53 and $41.97. The company would like to tell toy manufacturers to expect parents to spend an average of $40 on birthday gifts. Does the confidence interval support this claim? The company used the same data to compute another confidence interval this time concluding the mean amount spent was between $35.63 and $42.86.  In this second confidence interval, is the confidence level higher or lower than 95%.  Briefly explain. The company wants to do a similar study with a different sample.  They want to keep the confidence level at 95% but make the confidence interval narrower. What do you recommend they do? A report five years ago stated that 35.5% of all state-owned bridges in a particular state were “deficient”, in need of repair. Believing this to be an overestimate an independent research group took a random sample of 107 state-owned bridges in the state and found 31 to be currently rated as being “deficient”. Test the research group’s claim using a 5% significance level. State the null and alternative hypotheses. State each hypothesis both verbally and mathematically. Statistical software indicates the test statistic is