Statistics Questions

In an election suppose that 45 of voters support creating a new fire district If we poll 193 of these voters at random the probability distribution for the proportion of the polled voters that support creating a new fire district can be modeled by the normal distibution pictured below Complete the boxes accurate to two decimal places Note The left box is 2 standard deviations below the mean The middle box is the mean And the right box is 2 standard

mom 1 20 points A circular tank on the surface of an elastic mass car distributed load of 8400 psf The radius of the tank is 50 feet What is the intensity of the vertical pressure A o due to the tank loading in lbs sq ft a at a point 100 ft below the center of the tank 10 9 1 8 1 AT CENTER z R 0 0 02 0 05 0 10 0 2 0 4 0 5 0 8 2 Aolq 1 0 9999 0 9998 0 9990 0 9925 0 9488 0 9106 0 7562 13 z R 1 0 1 5 2 0 2 5 3 0 4 0 5 0 Aolg 0 6465 0 4240 0 2845 0 1996 0 1436 0 0869 0 0571 R 50 Ft 9 8400 PSF Z 100 2 50

Researchers have been studying a certain species of ant They are interested in the amount of weight that an ant can lift A random sample of ants lifting various objects has resulted in the following data set mass lifted grams 10 73 10 57 10 89 10 34 10 81 10 34 10 85 10 76 The researchers would like to resample this sample with replacement in order to study how the sample mean might vary from sample to sample They decide to resample it 8 times Carry out this procedure and report your 8 sample means Report at least two decimals for each sample mean

19 The mayor of the city of May normally distributed random variable the probability that a randomly chose week n household has between 55 and 15 Find a zo such that P Z zo 0 36 Sketch and shade this on a normal curve 10

3 Provide both the equation and a sketch of the requested function Draw two full periods in your sketch Be sure to label your sketch appropriately so it can be verified to be a sketch of your equation Provide a sine or cosine function with period 3 and amplitude 12

Chapter 5 6 100 pts Name Continuous Random Variables and The Normal Curve Probability Statistics Multiple Choice Write a brief explanation for your choice Which of the following can be used to describe the distribution for a continuous random variable a Binomial Distribution c Poisson Distribution b Normal Distribution d Hypergeometric Distribution When working with a continuous random variable the outcomes are b estimated d None of these a counted c measured Which of the following is not a characteristic of the normal distribution a It is symmetric b It is bell shaped c Mean Median Mode d None of these The standard normal curve is a distribution with a 1 and 0 0 c u larger than b 0 and 0 1 d u usually larger than O 5 The area under the curve to the right of z 0 is b 1 0000 a 0 6816 c 0 5000 d 0

6 If z is a standard normal random variable the area between z 0 and z 1 2 compared to the area between z 1 2 and z 2 4 will be b smaller c the same a larger d Not Enough Info 7 The probability density function f x of a random variable X that is normally distributed is completely determined once the a mean and standard deviation of X are specified b mean and mode of X are specified c median and mode of X are specified d mean and median of X are specified 8 The exponential distribution is often concerned with a the number of failures in an experiment b the amount of time until an event occurs c the number of successes in an experiment d events that are equally likely to happen

20 A normal random variable x has an unknown standard deviation and mean 54 If the probability that x is less than 58 is 0 8944 find the standard deviation

19 The mayor of the city of Mayville was informed that household garbage pickup was a normally distributed random variable with 65 pounds and 0 9 pounds per week a Find the probability that a randomly chosen household has more than 55 pounds of garbage per week h Find the probability that a randomly chosen household has between 55 and 70

18 Suppose that the longevity of a light bulb is exponential with a mean lifetime 8 years a Find the probability that a light bulb lasts less than 1 year b Find the prob that a bulb lasts between 6 and 10 years

US Sebastian scores a 258 on a test where the class had 230 and 0 22 What new score round to hundredths would Sebastian have if that 258 was converted to a scale with 76 and 0 4

SHOW YOUR METHOD OF CA 9 The Sky Train from the terminal to the long term parking center is supposed arrive every 8 minutes The waiting times for the train are known to follow a Uniform distribution from 0 to 8 minutes a Sketch the given information b What is the average waiting time in minutes c Find the probability of waiting more than 7 minutes d Find the probability of waiting more than 7 minutes if the given person has already 14 minutes

17 Find the z value that corresponds to the following percentiles a 72nd percentile b 98th percentile Z Z

16 A normal random variable x has a mean 18 and probabilities of each x value a P x 16 5 b P x 15 c P 11 x 19 AGAIN Show your method of calculation

If scores for a school team were normally distributed with a mean 68 and a eviation 3 Determine the z score for a golfer who scored 65 ind the probability that a randomly selected golfer scored less than 65 and the probability that a randomly selected golfer scored between 60 and 70 10 Su parar

10 Suppose that the useful life of a particular car battery measured in months decays with parameter 0 025 We are interested in the life of the battery an Exponential distribution a X Exp of data b On average how long would you expect one car battery to last c Find the probability that a car battery lasts more than 36 months d Find the probability that a car battery lasts less than 30 months

11 Find the following probabilities for the Normal curve Show your method of calculation a P z 1 32 b P 0 8 z 1 5 c P Z 0 d P 1 57 z 1 57

1 To assess the effectiveness of the artificial marks the team selected 14 cattle herds in Botswana Within each herd adult cattle were randomly assigned into one of three treatment groups artificial eyespots cross marked or unmarked The researchers have decided to use a 6 sided die in order to randomly assign the treatments to a herd of 50 cows One such die is shown here for you to use as a reference Describe a procedure which uses the die to assign each cow in the herd to one of the three treatments You can also write on the die rolling area to show your thinking

Given the two points write the equation in slope intercept form 4 1 and 8 8 4 1 8 8

A Food Marketing Institute found that 32 of households spend more than 125 a week on groceries Assume the population proportion is 0 32 and a simple random sample of 112 households is selected from the population What is the probability that the sample proportion of households spending more than 125 a week is less than 0 33 There is a probability that the sample proportion of households spending more than 125 a week is less than 0 33 Round the answer to 4 decimal places

A California College Culinary Program offers the most delicious and affortable breakfast and lunch choices among the 152 Community Colleges in California Past data shows that 69 of their patrons order the 5 meals when they visited This week a random sample of 91 orders will be used to estimate the proportion of the 5 meals being ordered Please answer the following questions and show your answer to 4 decimal places if necessary a What is the distribution of p p NO b What is the probability that less than 66 of the orders were for the 5 meals c What is the probability that between 67 and 69 of the orders were for the 5 meals

The average amount of money spent for lunch per person in the college cafeteria is 6 18 and the standard deviation is 2 09 Suppose that 47 randomly selected lunch patrons are observed Assume the distribution of money spent is normal and round all answers to 4 decimal places where possible a What is the distribution of X X N 6 18 2 09 b What is the distribution of N 0 O 0 3049 O c For a single randomly selected lunch patron find the probability that this patron s lunch cost is between 6 2527 and 6 6152 d For the group of 47 patrons find the probability that the average lunch cost is between 6 2527 and 6 6152 e For part d is the assumption that the distribution is normal necessary O Yes No o

Option 1 Describe a time in the past year when you witnessed incivility at school Use the STAIRR method to provide a detailed and specific answer Option 2 Describe a time in the past year when you witnessed incivility at work Use the STAIRR method to provide a detailed and specific answer Option 3 Describe a time in the past year when you witnessed incivility at a volunteer opportunity Use the STAIRR method to provide a detailed and specific answer Your Name Which option are you choosing to answer Situation Task this is an overview of the circumstance Action Intent Result Reflection Type your answers below in proper sentence format

In an election suppose that 55 of voters support a new tax on fast food If we poll 160 of these voters at random the probability distribution for the proportion of the polled voters that support a new tax on fast food can be modeled by the normal distibution pictured below Complete the boxes accurate to two decimal places 0 Note The left box is 2 standard deviations below the mean

On a planet far far away from Earth IQ of the ruling species is normally distributed with a mean of 108 and a standard deviation of 14 Suppose one individual is randomly chosen Let X IQ of an individual a What is the distribution of X X N108 14 OF OF b Find the probability that a randomly selected person s IQ is over 113 answer to 4 decimal places Round your c A school offers special services for all children in the bottom 6 for IQ scores What is the highest IQ score a child can have and still receive special services Round your answer to 2 decimal places o q d Find the Inter Quartile Range IQR for IQ scores Round your answers to 2 decimal places Q1 Q3 IQR

Given the graph write the quation in slope intercept form 6 2 4 3 2 10 10 123456 2 7 b

tiven the point and slope write the equation in slope intercept form 3 3 slope N M 2 3

4 a 01 X Ho Sample size Number of full time students a Is there any evidence that the average salary for XYZ is higher than 43 S Decision H Critical Value s Computed Value s XYZ 48 15 49 12 Graph

Given the graph write the equation in slope intercept form 2 6 5 4 3 10 1 2 3 4 5 6

Given the two points write the equation in slope intercept form 4 2 and 10 5

write the equation in slope intercept form 6 3 slope H N

Given the graph write the equation in slope intercept form OP 6 5 4 3 20 1 2 3 4 5 6 123456 Pinter 6 2 6

3 A home furnishings store that sells bathroom furniture is conducting an end of month inventory of the beds mattress bed have 95 confidence that her estimate of the mean value is correct to within 95 On the basis of past experience she estimates that spring and frame in stock An auditor for the store wants to estimate the mean value of the beds in stock at that time She wants to the standard deviation of the value of a bed is 150 a How many beds should she select b Using the sample size selected in a an audit was conducted with the following results X 1 654 27 S 184 62 Construct a 99 CIE for population Mean Formula Graph Critical Values C L E

am4 2 sion Assuming x 9 n 81 p 4 Is there any evidence that sample proportion be less than 3 Test at the a H Critical Value s Computed Value s Graph

2 272 5 and S 25 Test at the a 10 Does an average box of cereal contain less than 268 grams of cereal A random sample of 81 boxes showed sample mean Ho Decision H Critical Value s Computed Value s Graph

The luncheon expense vouchers of the executives of a large advertising firm have a population mean 10 G S4 per person Below what dollar value will 99 of the sample means fall What proportion of the sample means will be between 8 and 12 What proportion of the sample means will be below 8 or above 12 What proportion of the cample incans will be below 8 What proportion of the sample means will be above 13

Warding Off Predators Attacks on livestock by predators are a common problem for ranchers A research team wanted to know if artificial marks placed on livestock could be a cost effective tool in warding off attacks To assess the effectiveness of the artificial marks the team selected 14 cattle herds in Botswana Within each herd adult cattle were randomly assigned into one of three treatment groups 1 artificial eyespots a 2 cross marked b or 3 unmarked c Over a period of 30 days the number of cattle in each herd attacked by predators wor recorded Did the researchers conduct an observational study or an experiment Explain how you know Observational Study Explain your thinking Experiment

Refer to the table below to calculate the net free energy change when anaerobic butyrate metabolism is coupled to methanogenesis 136 kJ mol TABLE 13 6 Syntrophy Reactions Producing and Consuming H Genus Reaction 3H reduces an oxidant HCO SO or NO3 Methanospirillum Desulfovibrio Desulfovibrio Syntrophic catabolism producing H Syntrophus Syntrophomonas 4H HCO3 H CH 3H O 4H SO H HS 4H O 4H NO3 2H NH 3H O Benzoate 7H O 3 acetate HCO3 3H 3H Butyrate 2H O 2 acetate H 2H kJ mol a 136 152 600 70 49 Oxidant for syntrophy HCO3 25 AG kJ mol b 5 So NO3 2 45 33 13 18 AG is the standard free energy change at pH 7 when the concentrations of reactants and products are the same PAG was the measured free energy change at pH 7 when syntrophic metabolism stopped Michael McInerney et al 2007 PNAS 104 7600 Ralf Cord Ruwisch et al 1988 Arch Microbiol 149 350 Bradley E Jackson and Michael J McInerney 2002 Nature

13 Consider a small collection of four letters A B C D Think of this collection as a small population How many samples of size two are possible if sampling is done with replacement Answer samples How many samples of size two are possible if sampling is done without replacement Answer samples Previous Answers 10 6

A population of values has a normal distribution with 228 3 and 79 9 a Find the probability that a single randomly selected value is greater than 235 9 Round your answer to four decimal places P X 235 9 b Find the probability that a randomly selected sample of size n 218 has a mean greater than 235 9 Round your answer to four decimal places P M 235 9

A population of values has a normal distribution with 50 4 and o 51 8 A random sample of size n 230 is drawn a What is the mean of the distribution of sample means H b What is the standard deviation of the distribution of sample means Round your answer to two decimal places OF

D The number of eyelashes of the bottom eyelid of a human is approximately normal with a standard deviation of 1 2 eyelashes The original data on the actual mean of the number of eyelashes was lost A random sample of 32 human lower eyelids gives the sum of eyelashes as 2 480 and a sum of the squares of the eyelashes as 225 200 Find a 95 confidence interval for the mean of the number of eyelashes on the lower eyelids of humans

c The number of spots on a dalmatian dog is approximately normally distributed Suppose the standard deviation is known to be 30 spots and the mean is unknown A survey of 26 dalmatian dogs was taken with the results of the sum of the spots was 3025 and the sum of the squares of the spots was 450 000 Find the 99 confidence interval for the mean of the number of spots on dalmatian dogs

A population of values has a normal distribution with u 105 6 and 92 7 A random sample of size n 221 is drawn Find the probability that a sample of size n 221 is randomly selected with a mean greater than 96 2 Round your answer to four decimal places P M 96 2

Use the given claim and test statistic to find the P value Claim The mean monthly rental for a studio in one city is 870 Test statistic z 0 76 O 0 2236 O 0 4472

A simple random sample of size n 40 is obtained from a population with a mean of 20 and a standard deviation of 5 Is the sampling distribution approximately normal Why Yes the sampling distribution is approximately normal because the sample size is greater than 30 Yes the sampling distribution is approximately normal because the population is normally distributed O No the sampling distribution is not approximately normal because the population is not normally distributed O No the sampling distribution is not approximately normal because the population mean is less than 30

Compute the value of an appropriate test statistic for the given hypothesis test and sample data Assume that the population is normally distributed and that the sample has been randomly selected Ho o 9 8 H 0 9 8 n 19 s 12 2 0 05 a OX 559 467 OX 22 408 O X 27 896

Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test i e describe the values of the test statistic that would result in rejection of the null hypothesis A store manager claims that the mean amount of time customers spend waiting in line is less than 3 7 minutes You wish to test this claim at the 0 05 level of significance The mean waiting time for a random sample of 56 customers is 3 5 minutes with a standard deviation of s 1 2 minutes What criterion would be used for rejecting the null hypothesis that 3 7 Reject Ho if test statistic 1 645 O Reject Ho if test statistic 1 96 or 1 96 O Reject Ho if test statistic 1 96 Reject Ho if test statistic 1 673

Test the given claim using the traditional method A public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes Karen took bus number 14 during peak hours on 18 different occasions Her mean waiting time was 7 5 minutes with a standard deviation of 1 6 minutes At the 0 01 significance level test the claim that the mean is less than 10 minutes O There is not sufficient evidence to support the claim that the mean is less than 10 minutes O There is sufficient evidence to warrant rejection of the claim that the mean is less than 10 minutes O There is not sufficient evidence to warrant rejection of the claim that the mean is less than 10 minutes O There is sufficient evidence to support the claim that the mean is less than 10 minutes

Should the statistician use a t distribution a normal distribution or neither to test the nul hypothesis The sample mean x bar for a data set is 3 36 s 0 376 and n 55 The data is approximately normal and ois unknown Ho M 3 326 H 3 326 O Neither O Normal distribution