MTH 220 Statistical Methods and Inference

An insurance company has 10000 automobile policyholders. If the expected yearly claim per policyholder is $260 with a standard deviation of $800, what is the expected total yearly claim of all 10000 policyholders? An insurance company has 10000 automobile policyholders. If the expected yearly claim per policyholder is $260 with a standard deviation of $800, what is the standard deviation of total yearly claim of all 10000 policyholders? An insurance company has 10000 automobile policyholders. If the expected yearly claim per policyholder is $260 with a standard deviation of $800, calculate the probability that the total yearly claim exceeds $2.8 million (= 2.8 x 106) The mean height of all the elderly women in a city is 160 cm and the variance of their heights is 36 cm2. If a sample of 50 elderly women is taken, what is the probability that their mean height will be within 1 cm of the mean height of the population of elderly women in the city? The mean height of all the elderly women in a city is 160 cm and the variance of their heights is 36 cm2. If a sample of 60 elderly women is taken, what is the probability that their mean height will be less than 158 cm? Studies have shown that "Melanoma", a form of skin cancer, kills 15% of Americans who suffer from the disease each year. Consider a sample of 10000 melanoma patients.  What is the expected value of y, the number of the 10000 melanoma patients who die of this affliction this year? Studies have shown that "Melanoma", a form of skin cancer, kills 15% of Americans who suffer from the disease each year. Consider a sample of 10000 melanoma patients. What is the variance of y, the number of the 10000 melanoma patients who die of this affliction this year? Studies have shown that "Melanoma", a form of skin cancer, kills 15% of Americans who suffer from the disease each year. Consider a sample of 10000 melanoma patients. What is the probability that y will exceed 1600 patients per year? The random variable Y has a Poisson distribution with mean 50. Compute the probability P(Y > 60). Which of the following statements is TRUE? The binomial distribution with parameters n and p may be usefully approximated by a normal distribution with the same mean and variance, N(np, npq), when both np and nq are at most 5. The binomial distribution with parameters n and p may be usefully approximated by a normal distribution with the same mean and variance, N(npq, np2), when both np and nq are at least 5. note that q = 1 - p. The Poisson distribution with parameter µ may be usefully approximated by a normal distribution with the same mean and variance, N(µ, µ), when µ is at least 30. The Poisson distribution with parameter µ may be usefully approximated by a normal distribution with the same mean and variance, N(µ, µ), when µ is at most 60.  It is important to model machine downtime correctly in simulation studies. Consider a single-machine-tool system with repair times (in minutes) that can be modeled by an exponential distribution mean = 60. Of interest is the mean repair time of a sample of 100 machine breakdowns. What is the probability that the mean repair time is no longer than 30 minutes? It is important to model machine downtime correctly in simulation studies. Consider a single-machine-tool system with repair times (in minutes) that can be modeled by an exponential distribution mean = 60. Of interest is the mean repair time of a sample of 100 machine breakdowns. What is the variance of the mean repair time? Suppose the average cost of a gallon of unleaded fuel at gas stations is $1.897. Assume that the standard deviation of such costs is $0.15. Suppose a random sample of n = 100 gas stations is selected from the population and the cost per gallon of unleaded fuel is determined for each. Consider the "sample mean cost per gallon". What is the approximate probability that the sample has a mean fuel cost between $1.90 and $1.92?   When we construct the 99% confidence intervals for the population mean (* denoting a confidence level of 99%), what is the value of Za/2 used in the computation? Group of answer choices 1.96 2.011 1.645 2.575  A study was conducted to estimate the mean annual expenditure of SUSS students on textbooks. Assuming that the expenditure is normally distributed with a population standard deviation $250. Suppose a random sample of 50 students is drawn and the sample mean is calculated to be $1000. What is the 95% confidence interval of the population mean? Group of answer choices 845.2  ≤   μ   ≤  1024.3 930.7  ≤   μ   ≤  1069.3 910.8 ≤   μ   ≤  1055.2 975.6 ≤   μ   ≤  1077.3 Assume that the time patients spend waiting to see the doctor in the polyclinic is normally distributed. A random sample of 5 observations give the following sample statistics --- sample mean = 30 minutes and sample variance = 86. Suppose the population variance is unknown, what is the 90% confidence interval of the population mean? Group of answer choices 19.55 ≤  μ  ≤ 37.1 21.16 ≤  μ  ≤ 38.84 18.40 ≤  μ  ≤ 32.97 19.93 ≤  μ  ≤ 35.66 The following data from a random sample represents the average daily energy intake in kJ for each of eleven healthy women: 5260 5470 5640 6180 6390 6515 6805 7515 7515 8230 8770 Interest centred on comparing these data with an underlying mean daily energy intake of 7725 kJ This was the recommended daily intake. Departures from this mean in either direction were considered to be of interest. Assuming that the population is normal and the population variance is unknown. An appropriate two-tailed hypothesis test at the 5% level of significance was conducted. The null hypothesis is H0: m = 7725. Which test is appropriate to apply for this one population hypothesis problem?  Group of answer choices Z test F test The maximum likelihood method t  test The following data from a random sample represents the average daily energy intake in kJ for each of eleven healthy women 5260 5470 5640 6180 6390 6515 6805 7515 7515 8230 8770