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 127127 is 11. 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. ?x 11 22 33 44 55 66 77 88 99 ?(?)P(x) 0.3010.301 0.1760.176 0.1250.125 0.0970.097 0.0790.079 0.0670.067 0.0580.058 0.0510.051 0.0460.046 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. ?(?)E(X) =     Select the statement that best describes the interpretation of the expected value of the Benford's law probability distribution. The expected value is the leading significant digit that shows up the most in a set of numerical values. The expected value is calculated by taking an unweighted average of all values of ?x. The expected value is the average value of the leading significant digits in any set of numerical values that follow Benford's law. The expected value is sum of the probabilities associated with each leading digit divided by the number of possible leading digits. The expected value is the long‑run average value of the leading significant digits of a set of numerical values.

An institute reported that 70​% of its members indicate that lack of ethical culture within financial firms has contributed most to the lack of trust in the financial industry. Suppose that you select a sample of 100 institute members. The probability is 97​% that the sample percentage will be contained within what symmetrical limits of the population​ percentage? The probability is 97​% that the sample percentage will be contained above ______​% and below________​%.

Let X = {Email, In Person, Instant Message, Text Message}; P(Email) = 0.06 P(In Person) = 0.55 P(Instant Message) = 0.24 P(Text Message) = 0.15   Is this model a probability distribution? A. Yes. B. No. C. Maybe.

A study by a reputable research organization found that when presented with prints from the same​ individual, a fingerprint expert will correctly identify the match 91​% of the time. In​ contrast, a novice will correctly identify the match 77​% of the time. Consider a sample of seven different pairs of​ fingerprints, where each pair is a match. Complete parts a and b below.         a. What is the probability that an expert will correctly identify the match in all seven pairs of​ fingerprints?   The probability is enter your response here. ​(Round to four decimal places as​ needed.)   b. What is the probability that a novice will correctly identify the match in all seven pairs of​ fingerprints?   The probability is enter your response here. ​(Round to four decimal places as​ needed.)

A random sample of adults was asked about their highest education level completed. The distribution of results is shown in the table.   What is the probability that the highest level of education of an adult is a high school diploma, given that they have completed at least one of the education levels shown? 0.04 0.16 0.47 0.84

According to an​ airline, flights on a certain route are on time 80​% of the time. Suppose 17 flights are randomly selected and the number of​ on-time flights is recorded. The probability that fewer than 11 flights are on time is ___?____ (Round to four decimal places as needed)

A certain group of women has a 0.06% rate of red/green color blindness. If a woman is randomly selected, what is the probability that she does not have red/green color blindness?