Problem. In many naturally occurring tables of numerical data, it is observed thatthe leading (i.e., leftmost) digit is not uniformly distributed among {1, 2, ..., 9}, butthe smaller digits appear more frequently that the larger ones. In particular, the digitone leads with a frequency close to 30% whereas the digit nine leads with a frequencyclose to only 4%. Explain.

Introduction. In this question we will explain the statement given in the question.

Answered: Problem. In many naturally occurring…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The price of a share of stock divided by the company's estimated future earnings per share is called the P/E ratio. High P/E ratios usually indicate "growth" stocks, or maybe stocks that are simply overpriced. Low P/E ratios indicate "value" stocks or bargain stocks. A random sample of 51 of the largest companies in the United States gave the following P/E ratios†. 11 35 19 13 15 21 40 18 60 72 9 20 29 53 16 26 21 14 21 27 10 12 47 14 33 14 18 17 20 19 13 25 23 27 5 16 8 49 44 20 27 8 19 12 31 67 51 26 19 18 32 (a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to four decimal places.) x = s = (b) Find a 90% confidence interval for the P/E population mean ? of all large U.S. companies. (Round your answers to one decimal place.) lower limit upper limit (c) Find a 99% confidence interval for the P/E population mean ? of all large U.S.…
Suppose that, at the end of last semester, Marie gave her introductory statistics class a final exam. After grading these exams, she created a histogram illustrating the distribution of exam scores for the 70 students in the class. Each of the bars in this histogram includes only the left endpoint of the interval, except for the bar representing scores between 90 and 100 points, which also includes the right endpoint. What percentage of students scored between 60 and 80 points on the exam? Round your answer to the nearest tenth of a percent. Number of students who scored at least 80 points = students Percentage of students who scored between 60 and 80 points = %
A researcher is interested in the relationship between birth order and personality. A sample of n= 100 people is obtained, all of whom grew up in families as one of three children. Each person is given a personality test, and the researcher also records the person’s birth-order position (1st born, 2nd, or 3rd). The frequencies from this study are shown in the following table. On the basis of these data, can the researcher conclude that there is a significant relation between birth order and personality? Test at the .05 level of significance. Birth Position 1st 2nd 3rd Outgoing 13 31 16 Reserved 17 19 4 The expected frequencies for Outgoing, Birth Position 1st is: The expected frequencies for…
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10) An airline recorded the number of on-time arrivals for a sample of 100 flights each day. The boxplot below summarizes the records data for one year. 70 80 90 100 Number of On-Time Arrivals Based on the boxplot, which of the following statements must be true? (A) The range of the number of on-time arrivals is greater than 90. (B) The interquartile range of the number of on-time arrivals is 22. (C) The number of days that had at least 80 on-time arrivals is greater than the number of days that had at most 76 on-time arrivals. (D) The number of days that had from 76 to 80 on-time arrivals is equal arrivals. (E) The difference between the median and the lower quartile for the number of on-time arrivals is less than 2. the number of days that had at 76 on-time 11) Which of the following can outliers affect significantly? I. Mean II. Median III. Standard deviation IV. Range V. Interquartile range (A) I, III, and V (B) II and IV (C) I and V (D) I, III, and IV (E) None of these choices…
Does it seem to you that people tend to be absent more on some days of the week than on others? Recently, a major biotechnology firm collected data with the hope of determining whether or not its employees were more likely to be absent on some weekdays than on others. The firm examined a random sample of 130 employee absences. The distribution of these 130 absences is shown in the table below. The observed frequency for each category (each weekday) is shown in the first row of numbers. The second row of numbers contains the frequencies expected for a sample of 130 employees if employee absences at the firm are equally likely on each of the five weekdays. The bottom row of numbers contains the following value for each of the categories.
Assume we have data on all of the the students in our class. There are 25 students in the class. There are 4 seniors in the class and there are 6 juniors. What is the cumulative relative frequency of juniors and seniors?
(b) 9 Five pennies were tossed 1000 times, and at each toss the number of heads was observed. The number of tosses during which 0, 1, 2, 3, 4, and 5 heads were obtained is shown in Table 2.12. (a) Graph the data of Table 2.12. (b) Construct a table showing the percentage of tosses resulting in a number of heads less than 0, 1, 2, 3, 4, 5, or 6. (c) Graph the data of the table in part (b). Table 2.12 Number of Tosses (frequency) Number of Heads 0 38 1 144 2 342 3 287 4 164 25 1000 Total
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12. The following dotplot shows the results from a previous class. The average word 1 is the Average Word length when students selected their own words and Average Word 2 is when the words were randomly selected. Variable 7 Average Word-2800 88..... Average Word-1- The population mean for word length is 4.3 letters. Comment on results from both graphs and the ability to predict the population mean from a sample. Your answer should be a college level paragraph that consists of a topic sentence, supporting sentences and a concluding sentence.

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