Determine the required value of the missing probability to make the distribution a discrete probability distribution.
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To find the value of P(4) we will use the fact that sum of probabilities of possible outcome is always one.
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- The following are the probability distributions for the cost of textbooks in the fall semester for two different majors. Each probability represents the chance that the total cost of a student's books will be the given amount. Calculate the absolute difference in the expected cost of textbooks for the fall semester for these two majors. Express your answer rounded to two decimal places. Cost of Textbooks (in dollars) for Business Majors X 431.00 510.00 625.00 X Cost of Textbooks (in dollars) for Chemistry Majors 500.00 601.00 P(X = x) 649.00 0.23 0.56 0.21 P(X = x) 0.18 0.52 0.30A professor knows that her statistics students' final exam scores have a mean of 80 and a standard deviation of 10.3. In his class, an "A" is any exam score of 90 or higher. This quarter she has 23 students in her class. What is the probability that 6 students or more will score an "A" on the final exam?Hint: You will need to use your knowledge of normal probability distributions to determine the probability of one individual getting an A and then use your knowledge of binomial distributions to determine the probability of 6 students or more out of 23 students getting an A.prob = _______________Report your final answer accurate to 4 decimal places. Do not round any of the numbers in this calculation until the very end of the problem!A professor knows that her statistics students' final exam scores have a mean of 80 and a standard deviation of 12.2. In her class, an "A" is any exam score of 90 or higher. This quarter she has 25 students in her class. What is the probability that 7 students or more will score an "A" on the final exam?Hint: You will need to use your knowledge of normal probability distributions to determine the probability of one individual getting an A and then use your knowledge of binomial distributions to determine the probability of 7 students or more out of 25 students getting an A.prob = ____________Report your final answer accurate to 4 decimal places. Do not round any of the numbers in this calculation until the very end of the problem!
- What is the difference between discrete and continuous probability distributions? What are six situations in which a variable of interest may be considered either continuous or discrete?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 μ = 9.2 mg/L with 95% of the data ranging from 5.4 mg/L to 13.0 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume xhas a probability distribution that is approximately normal. (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 8 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 12…Benford's law, also known as the first-digit law, represents a probability distribution of the leading significant digits of numerical values in a data set. A leading significant digit is the first occurring non-zero integer in a number. For example, the leading significant digit in the number 127 is 1. Let this leading significant digit be denoted x. Benford's law notes that the frequencies of x in many datasets are approximated by the probability distribution shown in the table. 1 3 4 5 7 8 9. P(x) 0.301 | 0.176 | 0.125 | 0.097 0.079 | 0.067 0.058 0.051 | 0.046 Determine E(X), the expected value of the leading significant digit of a randomly selected data value in a dataset that behaves according to Benford's law? Please give your answer to the nearest three decimal places.
- 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 μ = 9.8 mg/L with 95% of the data ranging from 6.6 mg/L to 13.0 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. (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 8 mg/L? (Round your answer to four decimal places.) 0.7734 (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 12…Show that the Geometric probability distribution, with parameter p, is a valid discrete probability distribution.Suppose that you take a sample of size 40 from a population that is normally distributed. Can the sampling distribution of x̄ be approximated by a normal probability distribution? What if the population was not normally distributed, can the sampling distribution of x̄ be approximated by a normal probability distribution?
- 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 μ = 9.9 mg/L with 95% of the data ranging from 6.3 mg/L to 13.5 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. (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 8 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 12…A random sample statistic will have a probability distribution that is its sampling distribution True False