# Probability Questions and Answers

Statistics

ProbabilityFor 20 25 Use Table A Standard Normal Distribution to find the proportion of observations that satisfies each of the following statements In each case shade the area under the curve that is the answer to the question 20 23 3 2 1 0 z is less than 1 83 4 2 1 1 2 3 0 3 1 2 z is between 1 42 and 2 68 3 21 3 2 1 0 1 2 z is greater than 2 18 24 2 1 0 1 z is greater than 0 51 2 3 3 22 25 2 1 0 1 2 3 z is less than 0 33 3 2 1 0 1 2 3 z is between 2 and 1 53

Statistics

ProbabilityA random process Y t has the power spectral density a Find the autocorrelation function of Y t b Find the average power in the process Y t Question 2 16 Syy W W 64 Let P 0 85 0 261 0 15 0 74 Hint P X X a Find stable probability matrix P

Statistics

ProbabilityUse the data in the following table which lists drive thru order accuracy at popular fast food chains Assume that orders are randor selected from those included in the table Drive thru Restaurant C 235 36 A Order Accurate 337 Order Not Accurate 37 If two orders are selected find the probability that they are both accurate Complete parts a and b below B 274 52 D 121 12 a Assume that the selections are made with replacement Are the events independent The probability is 0 7672 The events are independent Do not round until the final answer Round to four decimal places as needed b Assume that the selections are made without replacement Are the events independent The probability is The events independent Do not round until the final answer Round to four decimal places as needed

Statistics

Probability2 Let the function f x be defined by f 0 1 and f x for a 0 One can show that the function f is infinitely many times differentiable and that f equals to its Taylor series about x 0 Consider the function g t where a t e 1 a Then the power series representation of g t about t 0 is az t Write x y Write x y Write x y z Write e for e Write cos z for cos z parenthesis are required Write acos z for arccos z parenthesis are required Write In z if Inz parenthesis are required for for ay is required for and parenthesis are required I da

Statistics

ProbabilityA company produces steel rods The lengths of the steel rods are normally distributed wi 262 2 cm and a standard deviation of 0 7 cm Answer the following to the nearest tenth of a cm Find P34 which is the length separating the shortest 34 rods from the longest 66 I rm

Statistics

ProbabilityThe table below is a record of the number of miles driven between stops for gas and the amount of money spent to fill up the gas tank in Amelia s car over several months Miles Driven x Cost to Fill up y 292 Table U s Gas Fill Up Log 293 313 305 345 276 337 21 85 22 60 24 15 22 90 26 21 21 24 25 02 Copy Data Step 2 of 2 If Amelia needs to drive 311 miles home from college and leaves with a full tank how much should she budget to fill up when she gets home Assume the regression equation is appropriate for prediction Round your answer to the nearest cent

Statistics

ProbabilitySolve the problem and find the equation Determine the type of conic section and sketch the graph 2 4 x 2 3 xy 2 y 10 3 x 10y 5

Statistics

ProbabilityYears elapsed Total population billions Population 1 2 Year 11 10 9 4 3 2 1 World population milestones in billions 0 9 1804 1927 1959 1974 1987 1999 2011 2026 2042 123 32 13 12 12 15 16 T 2 billion 1928 15 7 billion 2010 6 billion 1998 O 5 billion 1986 3 billion 1959 4 billion 1973 O 9 billion 2037 8 billion 2022 1800 2022 estimates Median projection 80 prediction interval 95 prediction interval 1 What is the trend shown in time needed to add another billion to the human population 2 Why is causing the trend to behave the way it does 3 Identify describe 3 ways the trend in human population growth especially since the 1970s negatively affects marine populations

Statistics

ProbabilityA Find the sample standard deviation rounding to one decimal place 5 9 13 7 15 5 14 7 10 OA 3 8 OB 12 9 C 14 5 OD 3 6

Statistics

ProbabilitySuppose that percent offer is believed to be normally distributed with a mean of 0 30 and a standard deviation of 0 15 a What is the probability that a randomly selected person will offer at least 0 50 of their endowment I b What is the probability that a randomly selected person will offer less than 0 44 of their endowment c What is the probability that a randomly selected person will offer between 0 20 and 0 40 of their endowment

Statistics

ProbabilitySuppose that to assign participants to their experimental condition the researchers used an 8 sided die where each number represents one of the eight different combinations of wealth and stakes Determine the expected value variance and standard deviation for the probability distribution of the random variable x where x is the outcome of the roll of an 8 sided die Provide a graph representing this probability distribution

Statistics

Probabilitya company needs new employees through an employee selection test from all test takers 20 of the participants pass a random sample 15 people Find the probability that there are exactly 5 participants and maximum of 3 people 7 40 02 AM

Statistics

ProbabilityA coin operated drink machine was designed to discharge a mean of 7 fluid ounces of coffee per cup In a test of the machine the discharge amounts in 14 randomly chosen cups of coffee from the machine were recorded The sample mean and sample standard deviation were 7 08 fluid ounces and 0 25 fluid ounces respectively If we assume that the discharge amounts are approximately normally distributed is there enough evidence to conclude that the population mean discharge u differs from 7 fluid ounces Use the 0 10 level of significance Perform a two tailed test Then answer the questions below Carry your intermediate computations to three or more decimal places a State the null hypothesis Ho and the alternative hypothesis H Ho H b Determine the type of test statistic to use Z t Chi Square F Degrees of freedom if applicable c Find the value of the test statistic Round to three or more decimal places d Find the p value Round to three or more decimal places e Can we conclude that the mean discharge differs from 7 fluid ounces Yes No

Statistics

ProbabilityEach year advertisers spend billions of dollars purchasing commercial time on network sports television In the first 6 months of 1988 advertisers spent 1 1 billion Who were the largest spenders A recent article listed the top 10 leading spenders in millions of dollars Calculate the sample variance rounding to two decimal places Company A 73 3 Company F Company B 62 9 Company G Company C 56 8 Company H 55 2 Company I 28 3 Company J Company D Company E OA 420 43 B 20 50 24 4 24 1 21 5 22 8 20 6 www

Statistics

ProbabilityThe following data represent the bachelor degrees of CEOs at area small businesses Determine the mode des Degree Number Accounting Business Liberal Arts Marketing Other A marketing B accounting C business P no mode 27 43 13 26 15