# Statistics Topics

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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

StatisticsFor 3 9 The mean weight of adult American men is 180 pounds with standard deviation of 25 pounds The weights are approximately normally distributed Use the 68 95 99 7 Rule to approximate each of the following 3 Using the values given above label the normal curve at the right with the numerical values for u a 20 and 30 4 What percent of all adult American men have a weight less than 130 pounds 5 What percent of all adult American men have a weight between 130 and 205 pounds 6 What percent of all adult American men have a weight less than 230 pounds 7 What percent of all adult American men have a weight less than 105 pounds 8 The heaviest 16 of all men in weight weigh more than how many pounds 9 What weight separates the lowest 2 5 of all American men in weight from the remaining weights

Statistics

StatisticsFor 26 28 Find the value of z from the standard normal distribution that satisfies each of following conditions Use the value of z from Table A that comes closest to satisfying the condition 26 Area is 0 0630 N z 27 z N Area is 0 2981 28 Z Z z Area is 0 5035

Statistics

StatisticsFor 10 17 Elephants have the longest pregnancy of all mammals One species of elephant has a mean gestation period of 525 days and standard deviation of 32 days Pregnancy length follows an approximately normally distribution Use the 68 95 99 7 Rule to approximate each of the following 10 Using the values given above label the normal curve at the right with the numerical values for o 20 and 30 11 The longest 16 of all elephant pregnancies last at least how many days 12 The middle 68 of all elephant pregnancies last between and days 13 Only 2 5 of all elephant pregnancies last longer than days 14 What percent of elephant pregnancies last less than 461 days 15 What percent of elephant pregnancies last between 525 and 557 days 16 What percent of elephant pregnancies last between 493 and 589 days 17 What percent of elephant pregnancies last less than 557 days

Statistics

StatisticsRULE INTERPRETING Z SCORES 1 If a person has a negative z score did the person score higher or lower than the mean 2 If a person has a negative z score it does not always mean that the person did not do well Name a sport where having the lowest z score would be the most desirabla At Name

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

StatisticsLet H be the set of polynomials a Give two different examples of polynomials in H example 1 p x example 2 g x b Give two different examples of polynomials from P3 which are not in H example 1 p x example 2 g x c Complete the following statements to determine if H is a subspace of P3 0 in H q x H p P3 P 2 0 His under vector addition If it is not closed enter two polynomials p q E H below whose sum is not in H If it is closed then leave the following spaces blank p x His under scalar multiplication If it is not closed enter a scalar k and polynomial r H below whose product is not in H If it is closed then leave the following spaces blank k and r x

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

StatisticsThree forces are acting on a modern streetlamp at points A B and C a Express the three forces acting at points A B and C as Cartesian force vectors in Sl units b Compute the resultant force vector written as a Cartesian force vector c Compute the magnitude of the resultant force vector you found in part d d Convert your answer in part d to the US customary system of units FPS 8 m 2 1 2 4 m 2 4 m A y 45 650 N 2 4 m 8 kN B 12 kN

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

StatisticsA researcher wants to know how registered voters in her state feel about health care She obtains a list of 2152 registered voters in her state selects 700 of them at random and emails a questionnaire to them 149 questionnaires are returned Of these 73 stated that they believe that the current health care program needs to be completely overhauled Classify the following groups a the population or the sample for this particular study If a group does not belong in either category leave it unplaced Population the 149 registered voters who returned the questionnaire the 73 who stated that the current health care program needs to be completely overhauled Answer Bank the 700 registered voters who were randomly chosen all registered voters in the researcher s state 21 the proportion of all registered voters in the researcher s state who believe that the current health care program needs to be completely overhauled Sample the 2152 registered voters whose names were obtained all registered voters