Consider the sample space given below.A die is a cube with six sides on which each side contains one to six dots. Suppose a blue die and a gray die are rolledtogether, and the numbers of dots that occur face up on each are recorded. The possible outcomes of the sample space Sare listed as follows, where in each case the die on the left is blue and the one on the right is gray.S = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36,41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66}Let E be the event that the sum of the numbers showing face up is 8. Write E as a set. (Enter your answer in set-rosternotation. Enter EMPTY or Ø for the empty set.)E =What is the probability of E?Enter a fraction, integer, or exact decimal. Do not approximate.

We can solve this using probability

Answered: Consider the sample space given below.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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In a memory test, the test subjects are given a large number and are asked to memorize it. Historical records show that 80% of test subjects pass the test. To pass the test, a subject must exactly repeat all the digits in the number after two hours. A random sample of 625 people to take the memory test is going to be chosen. Let p be the proportion of people in the sample who pass the test. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of P. 0 (b) Find the standard deviation of p. 0 (c) Compute an approximation for P(P >0.84), which is the probability that more than 84% of the people in the sample pass the test. Round your answer to four decimal places. 0 X
Part A: There is a population of five people. They were each asked how many movies they saw in the last year. Amy saw one (1), Bob saw seven (7), Clara saw thirteen (13), Dora saw nineteen (19), and Earl saw twenty-five (25). Looking at every single possible sample of size three (with replacement). First column will be a list of every single sample (e.g., Amy, Amy, and Amy – or AAA – Amy, Amy, and Bob – or AAB – et cetera). The second column will list the mean of each sample.The third column will list the variance of each sample (using N in the denominator); and the fourth column will list the variance of each sample (using N-1 as the denominator). Calculate the means of the last three columns. To calculate the averages of the columns, put the data in a frequency table and then calculate the mean using the table. Calculate the variance of the population. Look at the values of the numbers. Which one of these means is special? Why? This will have six distinct parts: 1) the…
The University of Chicago's General Social Survey (GSS) is the nation's most important social science sample survey. For reasons known only to social scientists, the GSS regularly asks a random sample of people their astrological sign. Here are the counts of responses from a recent GSS of 4344 people: Sign Aries Taurus Count 321 360 Sign Libra Scorpio Count 392 329 Gemini 367 Sagittarius 331 Cancer 374 Capricorn 354 Leo 383 Aquarius 376 Virgo 402 Pisces 355 We want to test Ho: All 12 astrological signs are equally likely versus Ha: All 12 astrological signs are not equally likely. Use a chi-square goodness-of-fit test to compute a test statistic and P-value. Do these data provide convincing evidence at the 1% significance level that all 12 signs are not equally likely? Because the P-value of 0.6562 > 0.05, we cannot reject the null hypothesis. We cannot conclude that all 12 signs are not equally likely. Because the P-value of 0.0487 > 0.01, we cannot reject the null hypothesis. We…
Please help. Suppose we roll a regular six die three times.
A group of 11 students was selected at random and asked for their high school GPA and their freshmen GPA in college the subsequent year. The results were: Student High School GPA Freshmen GPA 1 2.0 1.6 2 2.2 2.0 3 2.6 1.8 4 2.7 2.8 5 2.8 2.1 6 3.1 2.0 7 2.9 2.6 8 3.2 2.2 9 3.3 2.6 10 3.6 3.0 We would like to know whether there is a linear relationship between the high school GPA and the college freshmen GPA, and we would like to be able to predict the freshmen GPA, if we know that the high school GPA of another student is, say, 3.4. Provide the two requested scatter plots for this data (put college freshman GPA on the Y (vertical) axis!). a) What would be your approximate 95% prediction interval for question (g)? b) Show your scatterplot with the predicted trend line below
Given a population of N=93, starting in row 29 of the table of random numbers, and reading across the row, select a sample of n=15 a. without replacement. b. with replacement. Column Row 00000 00001 11111 11112 22222 22223 33333 33334 12345 67890 12345 67890 12345 67890 12345 67890 28 06873 21440 75593 41373 49502 17972 82578 16364 29 12478 37622 99659 31065 83613 69889 58869 29571 30 57175 55564 65411 42547 70457 03426 72937 83792 31 91616 11075 80103 07831 59309 13276 26710 73000 32 78025 73539 14621 39044 47450 03197 12787 47709 Choose the correct answer below. A. 12, 47, 83, 76, 22, 99, 65, 93, 10, 65, 83, 61, 36, 98, 89 B. 12, 47, 83, 76, 22, 65, 93, 10, 61, 36, 89, 58, 86, 92, 71 C. 47, 83, 76, 22, 99, 65, 93, 10, 65, 83, 61, 36, 98, 89, 58 D. 83, 76, 22, 99, 65, 93, 10, 65,…
. List the 10 possible samples (without replacement) of size 2 that can be obtained from the population of five officials. Lieutenant Governor (L) Secretary of State (S) Attorney General (A) Representative (R) Press Secretary (P) b. If a simple random sampling procedure is used to obtain a sample of two officials, what are the chances that it is the first sample on your list in part (a)? the secondsample? the tenth sample?
Superpowers A total of 415 children from the United Kingdom and the United States who completed a survey in a recent year were randomly selected. Each student's country of origin was recorded along with which superpower they would most like to have: the ability to fly, ability to freeze time, invisibility, superstrength, or telepathy (ability to read minds). The data are summarized in the following table. Country U.K. U.S. Fly 54 45 Freeze time 52 44 Invisibility 30 37 Superpower 20 23 Superstrength Telepathy 44 66 a. What proportion of students in the sample are from the United States? b. Find the distribution of superpower preference for the students in the sample using relative frequencies. c. What percent of students in the sample are from the United Kingdom and prefer telepathy as their superpower preference?
need help
. Assume that the box contains balls numbered from 1 through 28, and that 3 are selected. A random variable X is defined as 3 times the number of odd balls selected, plus 4 times the number of even. How many different values are possible for the random variable X?

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