The number of errors in any page of a 10-page report is Poisson distributed with mean 5. Suppose further that errors are independent. The expected number of pages in the report with more than two errors is equal to
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- Suppose that the time in minutes it takes a student to complete an assignment is normally distributed with a mean 55 and variance 100 then the 35th percentile of the average time it takes a random sample of 49 students to complete the assignment is closest to О а. 51. O b. 59. О с. 49. O d. 54. О е. 56.4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (µ = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? COr is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. %3D c. Which test statistic and sampling distribution under the null should we use? O i. z-score; standard Normal O ii. t-statistic; Student'stAn improved battery is being developed by a start-up company, which will be sent to the smartphones manufacturer. Suppose that the charging time for the old battery is normally distributed with a mean on 45 minutes, while the charging time for the new battery is normally distributed with a mean of 30 minutes. Given the standard deviation of the old battery is 20 minutes and the new battery is 30 minutes, respectively. Twenty random samples of both batteries were tested. Find the probability of sample of the new battery is better than the old one.
- 4. Researchers working for a sports drink company would like to know if a new blend if its popular sports drink can help improve marathon runners' final running time. Marathon times, Y, are known to follow a Normal distribution. Suppose that runners using the old blend sports drink have a mean finishing time of 300 minutes (H = 300 minutes). A random sample of 20 runners was selected to use the new blend of sports drink in a marathon, finishing with an average time of 270 minutes and a standard deviation of 20 minutes (y = 270 min, s = 20 min). Can it be claimed that the new blend lowers finishing times? Or is it possible that random chance alone can explain the discrepancy? Carry out a hypothesis test of the true mean u using the 4- step procedure. Set your alpha-level to 0.05. a. Which is the correct null hypothesis? O i. Ho: µ = 300 min O ii: Ho: µ = 270 min %3D O ii. Ho: µ < 300 min iv: Ho: µ < 270 minIn a large city, researchers selected a random sample of 120 individuals who have multiple televisions in their house connected to a streaming device. Each individual was asked how many hours of streaming content they watch in a typical week. The sample had a mean of 12.5 hours. For which of the following populations is 12.5 hours a reasonable estimate of the mean hours of weekly streaming content watched? (A) All individuals who regularly watch streaming content (B) All individuals from this city who regularly watch streaming content (C) All individuals from this city with multiple streaming devices in their house (D) All individuals from this city with multiple streaming devices in their house who regularly watch streaming content (E) All 120 individuals in this city with multiple streaming devices in their home who regularly watch streaming content5. Suppose the time spent by a randomly selected student at a campus computer laboratory has a gamma distribution with mean 20 min and variance 80 min². (a) What are the values of a and B? (b) What is the probability that a student spends between 20 and 40 min at the laboratory? (c) Only 1% of students will spend more than how many minutes at the laboratory?
- Suppose that the weight of seedless watermelons is normally distributed with mean 6.9kg and standard deviation 1.9kg. Let X be the weight of a randomly selected seedless watermelon. Round to 4 decimal places. What is the median seedless watermelon weight?Suppose that the fraction of defective modems shipped by a data-communications vendor has an approximation beta distribution with a=5 and b=21. find the mean and variance of the fraction of defective modems per shipment What is the probability that a randomly selected shipment will contain at least 30 % defectives? What is the probability that a randomly selected shipment will contain no more than 5 % defectives?The service times for customers coming through a checkout counter in a retail store are independentrandom variables with mean 1.5 minutes and the variance 1.0. Approximate the probability that 100customers can be served in less than (a) 2 hours (b) 3 hours of total service time.
- 29. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 11.2 years, and standard deviation of 2.1 years. The 7% of items with the shortest lifespan will last less than how many years? (Show all work)A psychologist obtains a random sample of 20 mothers in the first trimester of their pregnancy. The mothers are asked to play Mozart in the house at least 30 minutes each day until they give birth. After 5 years, the child is administered an 1Q test. It is known that IQs are normally distributed with a mean of 100. If the IQs of the 20 children in the study result in a sample mean of 104.4 and sample standard deviation of 16, is there evidence that the children have higher IQs? Use the a= 0.10 level of significance. Complete parts (a) through (d). (a) Determine the null and alternative hypotheses. Ho: H = 100 Hy: H > 100 (b) Calculate the P-value. P-value = (Round to three decimal places as needed.) %3D Enter your answer in the answer box and then click Check Answer. 2 parts remaining Clear All Check Answer 80 888 112 F7 esc F4 F2 & @ %23 delete 7 8 9 2 3 4 { Q W E Y tab F G H K A D caps lock V B N M C - - .. .- つ くC NThe number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.08 flaw per square foot of plastic panel. Assume an automobile interior contains 10 square feet of plastic panel. If 10 cars are sold to a rental company, what is the probability that at most one car has any surface flaws? Express your answer with 4 significant figures.
