7. A function whose value is a real number determined by each element in the sample space - the set of all possible outcomes of an experiment. A. random variable B. probability distribution C. density function D. histogram
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- Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was u = 9.3 mg/L with 95% of the data ranging from 6.7 mg/L to 11.9 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal. In USE SALT (a) Use the 95% data range to estimate the standard deviation for oxygen demand. (b) An oxygen demand below 8 indicates that some organisms in the wetland environment may be dying. What is the probability that the oxygen demand will fall below mg/L? (Round your answer to four decimal places.) (c) A high oxygen demand can also indicate trouble. An oxygen demand above 12 may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed…he home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gave the following data for home run percentages. 1.6 2.4 1.2 6.6 2.3 0.0 1.8 2.5 6.5 1.8 2.7 2.0 1.9 1.3 2.7 1.7 1.3 2.1 2.8 1.4 3.8 2.1 3.4 1.3 1.5 2.9 2.6 0.0 4.1 2.9 1.9 2.4 0.0 1.8 3.1 3.8 3.2 1.6 4.2 0.0 1.2 1.8 2.4 (a) Use a calculator with mean and standard deviation keys to find and s (in percentages). (For each answer, enter a number. Round your answers to two decimal places.) = x bar =____________ %s =___________________ % (b) Compute a 90% confidence interval (in percentages) for the population mean μ of home run percentages for all professional baseball players. Hint: If you use the Student's t distribution table, be sure to use the closest d.f. that is smaller. (For each answer, enter a number. Round your answers to two decimal places.)lower limit ____________ %upper limit ____________ % (c) Compute a 99% confidence…In an election, suppose that 45% of voters support creating a new fire district. If we poll 202 of these voters at random, the probability distribution for the proportion of the polled voters that support creating a new fire district can be modeled by the normal distribution pictured below. The bell curve below represents the distribution of these sample proportions. The scale on the horizontal axis is the standard deviation of the sampling distribution. So each tick mark represents a distance of one standard deviation on the distribution, with the middle tick mark being the mean of the distribution. Complete the boxes accurate to two decimal places. Note that the second box is at the mean. The first box is two standard deviations below the mean, and the third box is two standard deviations above the mean. Complete the boxes accurate to two decimal places.
- Four coins are tossed, and the number of heads is recorded. Shade the region on the histogram that gives the indicated probability. P(x > 2) Which of the following shaded regions gives the indicated probability? (Type A, B, C, or D.) A) 0.5- 0.38- 0.25- 0.13- 0- 0.5- 0.38 0.25- 0.13- लट 0 1 2 3 4 01 2 3 4 B) D) 0.5- 0.38- 0.25- 0.13- 0- 0.5- 0.38 0.25 0.13- 0- 0 1 2 3 4 0 1 2 3 4Rem. A concerned parents group determined the number of commercials shown in each of the five children's programs over a period of time. Num of Commercials P(X = x 1.824 0.078 2.081 0.05 2.338 0.101 2.595 0.134 2.852 0.07 3.109 0.567 Consider the probability distribution table above. Determine the following: (a) Determine the mean = (b) Determine the Standard DeviationThe probability is 0.4 that a traffic fatality involves an intoxicated or alcohol-impaired driver or nonoccupant. In six traffic fatalities, find the probability that the number, Y, which involve an intoxicated or alcohol-impaired driver or nonoccupant is a. exactly three; at least three; at most three. b. between two and four, inclusive. c. Find and interpret the mean of the random variable Y. a. The probability that exactly three traffic fatalities involve an intoxicated or alcohol-impaired driver or nonoccupant is nothing. (Round to four decimal places as needed.) The probability that at least three traffic fatalities involve an intoxicated or alcohol-impaired driver or nonoccupant is nothing. (Round to four decimal places as needed.) The probability that at most three traffic fatalities involve an intoxicated or alcohol-impaired driver or nonoccupant is nothing. (Round to four decimal places as needed.) b. The probability that between two and four…
- The normal distribution curve can be used as a probability distribution curve for normally distributed variables. Group of answer choices False TrueWhen specifying the probability distribution for the input variables, which approach is most useful for capturing the full range of possible values in a simulation study? A. Using the actual data B. Using an empirical distribution C. Using a theoretical distributionA survey of almost 44,000 two-child families yielded the accompanying table. The probability distribution of x, the number of boys in a two-child family is given below. Find E(x) and give a practical interpretation of its value. Gender Configuration Proportion D Girl-girl (GG) Boy-girl (BG) Girl-Boy (GB) 0.215 0.267 0.256 P(x) 0.215 0.523 0.262 Boy-boy (BB) 0.262 Choose the correct answer below and fill in the answer box to complete your choice. (Round to three decimal places as needed.) O A. If a very large number of households were sampled, on average, there would be E(x) = boys. O B. If a very large number of two-child households were sampled, on average, there would be E(x) = boys. of getting a family with a boy. %3D O C. If a very large number of two-child households were sampled, there would be a probability of E(x) = O D. In the sample of 44,000 households, each household had E(x) = boys.