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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Question 5 Suppose X is binomially distributed with E[X]=120 and Var(X)=48. (Choose The correct answer) Then the parameters of the distribution are:Question 2:The lifetime of a semiconductor laser at a constant gower is normally distributed with a mean of 6950 hours and a standard deviation of 620 hours. a. What is the probability that a laser fails before 6060 hours? b. If 9 lasers are used in a product and they are assumed to fail independently, find the standard deviation of the average lifetime of these lasers. (unit: hours) c. If 9 lasers are used in a product and they are assumed to fail independently, what is the probability that there are exactly 4 lasers failing before 6060 hours?
- Question 10 Consider an operational process in a factory where widgets are produced. As the process is not perfect, errors sometimes happen, and the errors are either technical or human. Over the last 100 days, errors were observed and recorded. On any given day, there occurred zero to three (0 to 3) human errors and zero to three (0 to 3) technical errors. The frequency distribution of errors is given in the following contingency table. Number of human errors No. of Tech Errors 0 1 2 3 Total 0 8 6 4 4 22 1 5 8 9 10 32 2 4 5 10 8 27 3 0 3 4 12 19 Total 17 22 27 34 100 What is the probability of 0 technical errors given 3 human errors? State your answer as a decimal value rounded to two digits after the decimal point.QUESTION 9 The Department of Trade and Industry (DTI) conducted a survey to estimate the average number of employees per small and medium-sized enterprises (SME) in Free State. For a random sample of 144 SMEs in Free State, the DTI found that the average number of employees was 24.4. Assume that the population standard deviation is 10.8 employees and that the number of employees per SME is normally distributed. Using this information and rounding off the z or t values that you derive to 2 decimal places, the 95% confidence interval of the average number of employees per SME in Free State is for the lower limit andfor the upper limit. (Note: write your final answers to 3 decimal places and when writing your answer use "." (3.250) instead of "," (3,250) with no spaces between digits).Question 15 Consider an operational process in a factory where widgets are produced. As the process is not perfect, errors sometimes happen, and the errors are either technical or human. Over the last 100 days, errors were observed and recorded. On any given day, there occurred zero to three (0 to 3) human errors and zero to three (0 to 3) technical errors. The frequency distribution of errors is given in the following contingency table. Number of human errors No. of Tech Errors 0 1 2 3 Total 0 8 6 4 4 22 1 5 8 9 10 32 2 4 5 10 8 27 3 0 3 4 12 19 Total 17 22 27 34 100 What is the probability of 3 human errors on any given day? State your answer as a decimal value rounded to two digits after the decimal point.
- Question 13 Consider an operational process in a factory where widgets are produced. As the process is not perfect, errors sometimes happen, and the errors are either technical or human. Over the last 100 days, errors were observed and recorded. On any given day, there occurred zero to three (0 to 3) human errors and zero to three (0 to 3) technical errors. The frequency distribution of errors is given in the following contingency table. Number of human errors No. of Tech Errors 0 1 2 3 Total 0 8 6 4 4 22 1 5 8 9 10 32 2 4 5 10 8 27 3 0 3 4 12 19 Total 17 22 27 34 100 What is the probability of 3 technical errors on any given day? State your answer as a decimal value rounded to two digits after the decimal point.Question 7 - Part B If 25% of U.S. women have the height lower than 5.1 feet, and 55 % of U.S. women have the weight more than 165 pounds, then 165 is which percentile and 5.1 is which percentile? Write the percintile in the "th" form; ex, 9th percentile, 11th percentile.Question 3 The number of traffic accidents per day on a certain section of highway is thought to be Poisson distributed with a mean equal to 2.19. Assume accidents are independent. Based on this, how many traffic accidents should be expected during a period of one week? (Choose the Correct Answer)
- Question 5 Consider the diameters of cylindrical parts manufactured on a computer-controlled lathe.a) Suppose that the mean of the diameters is known to be 0.1 millimetres. Give an upper bound to the probability that the diameter of new part will exceed 0.11 mm.b) Suppose that the mean is unknown but the standard deviation is known to equal 0.002 mm. What can be said about the probability that the diameter of a new part will be within 0.006 mm of the unknown mean for that run?c) How many new parts should be made so as to ensure, with probability at least 0.75, that the average diameter would be within 0.001 mm of the unknown mean? Assume each part is made independently.Question 6: The following data are collected to study unemployment in a particular region in upstate New York. The first column shows the number of months unemployed and the second column shows the count of people in the study with the corresponing unemployment length. Let X be a random variable indicating the number of months a person is unemployed. a)Use the data to develop the probability mass function for X. b)Find the cumulative distribution function for X. c)Calculate the mean and standard deviation of X. Months Unemployed Number Unemployed 1 1029 2 1686 3 2269 4 2675 5 3487 6 4652 7 4145 8 3587 9 2325 10 1120Question 8In a particular river, a certain micro-organism occurs at an average rate of 10 per mililitre.A random sample of 0.5 litres of water is taken from a nearby stream and is found tocontain 3478 micro-organisms. Does this provide significant evidence, at the 5% level, ofa difference in the incidence of the micro-organisms between the stream and the river?
