Probability Questions and Answers

Suppose that we ve decided to test Clara who works at the Psychic Center to see if she really has psychic abilities While talking to her on the phone we ll thoroughly shuffle a standard deck of 52 cards which is made up of 13 hearts 13 spades 13 diamonds and 13 clubs and draw one card at random We ll ask Clara to name the suit heart spade diamond or club of the card we drew After getting her guess we ll return the card to the deck thoroughly shuffle the deck draw another card and get her guess for the suit of this second card We ll repeat this process until we ve drawn a total of 15 cards and gotten her suit guesses for each Assume that Clara is not clairvoyant that is assume that she randomly guesses on each card Answer the following If necessary consult a list of formulas a Estimate the number of cards in the sample for which Clara correctly guesses the suit by giving the mean of the relevant distribution that is the expectation of the relevant random variable Do not round your response 0 b Quantify the uncertainty of your estimate by giving the standard deviation of the distribution Round your response to at least three decimal places

Car inspection Of all the registered automobiles in a city 11 fail the emissions test Fourteen automobiles are selected at random to under an emissions test Round the answers to at least four decimal places Part 1 of 4 a Find the probability that exactly five of them fail the test The probability that exactly five of them fail the test is 0 09523 Part 2 of 4 X

Suppose a simple random sample of size n 12 is obtained from a population with 68 and 16 a What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean Assuming the normal model can be used describe the sampling distribution x b Assuming the normal model can be used determine P x 72 1 c Assuming the normal model can be used determine P x 69 7 Click here to view the standard normal distribution table page 1 Click here to view the standard normal distribution table page 2 12 XB Normal with 68 and o 16 Oc Normal with 68 and o 16 b P x 72 1 Round to four decimal places as needed

The workers union at a certain university is quite strong About 96 of all workers employed by the university belong to the workers union Recently the workers went on strike and now a local TV station plans to interview a sample of 20 workers chosen at random to get their opinions on the strike Answer the following If necessary consult a list of formulas a Estimate the number of workers in the sample who are union members by giving the mean of the relevant distribution that is the expectation of the relevant random variable Do not round your response 0 b Quantify the uncertainty of your estimate by giving the standard deviation of the distribution Round your response to at least three decimal places 0 X

At a deli counter there are sandwiches with meat and 5 vegetarian sandwiches Bob is at the counter buying sandwiches for a picnic In how many ways can he choose 6 sandwiches if fewer than 3 must be vegetarian sandwiches If necessary consult a list of formulas

A catering service offers 12 appetizers 11 main courses and 5 desserts A customer is to select 10 appetizers 9 main courses and 2 desserts for a banquet In how many ways can this be done If necessary consult a list of formulas

e graph shows the age of students and the amount of daily study time they generally have in sell Daily Study Time minutes 11 What is the most likely 60 50 30 0 Daily Study Time 0 5 Age 15

CYU 5 2b Johnny has ret d to his favorite ice cream shop which serves 24 flavors 17 How many different three scoop bowls of ice cream can he order 2 How many different four scoop bowls of ice cream can he order 3 Let s use an example to explain what s happening when we count the number of bowls List out every three scoop cone choosing from the flavors Mint M Chocolate C Vanilla V and Strawberry S there are 24 different possibilities a

If necessary consult a list of formulas a A certain committee consists of 15 people From the committee a president a vice president a secretary and a treasurer are to be chosen In how many ways can these 4 offices be filled Assume that a committee member can hold at most one of these offices 0 b A company that makes crayons is trying to decide which 4 colors to include in a promotional mini box of 4 crayons The company can choose the 4 mini box colors from its collection of 65 colors How many mini boxes are possible 0

A toy company is going to issue new ID codes to its employees Each code will have one letter followed by five digits The digits 2 and 6 will not be used So there are 26 letters and 8 digits that will be used Assume that the digits can be repeated How many employee ID codes can be generated

Historically 2 percent of the stray dogs in Southfield are unlicensed On a randomly chosen day the Southfield city animal control officer picks up seven stray dogs What is the probability that fewer than two will be unlicensed Multiple Choice O O 8681 0076 3670

The coefficient of variation for a Poisson distribution with A 5 is Multiple Choice O O 35 2 percent 31 1 percent 58 9 percent 44 7 percent

Based on experience 60 percent of the women who request a pregnancy test at a certain clinic are actually pregnant In a random sample of 12 women what is the probability that at least 10 are pregnant Multiple Choice O O O 0639 0196 1424

Suppose X is binomially distributed with n 12 and 20 The probability that X will be less than or equal to 3 is Multiple Choice O O O 5584 7638 2362

In Quebec 90 percent of the population subscribes to the Roman Catholic religion In a random sample of eight Quebecois find the probability that the sample contains at least five Roman Catholics Multiple Choice O O O 9619 9950 0050

If X is a discrete uniform random variable ranging from one to eight find P X 6 Multiple Choice O O O 6250 5000 3750 7500

A charity raffle prize is 1 000 The charity sells 4 000 raffle tickets One winner will be selected at random At what ticket price would a ticket buyer expect to break even Multiple Choice O O O 1 00 0 25 0 50 0 75

Fish Weights The data in Table 5 give the average weights of pike for certain lengths Use 4 decimal places in all answers Table 5 Pike Length in Weight oz 10 14 18 22 26 30 34 38 44 52 5 12 26 44 72 108 154 210 326 522 A What cubic equation W x best fits the data where x is the length of a pike W x is the weight of the pike W x

If a school district takes a random sample of 63 Math SAT scores and finds that the average is 483 and knowing that the population standard deviation of Math SAT scores is intended to be 100 Find a 99 confidence interval for the mean math SAT score for this district Give your answers as decimals to two places What is the critical value 2 576 What is the margin of error 32 45 What is the confidence interval OF Part 2 of Part 3 of

n and Which of the following values could not O A 1 OB 1 032

nd ven a set of data and a correspondi

n and Two variables have a positive linear co

Discuss the difference between r and p Choose the correct answers below represents the o represents the Question critical value for the correlation sample correlation coefficient

A bus comes by every 11 minutes The times from when a person arives at the busstop until the bus arrives follows a Uniform distribution from 0 to 11 minutes A person arrives at the bus stop at a randomly selected time Round to 4 decimal places where possible a The mean of this distribution is b The standard deviation is c The probability that the person will wait more than 5 minutes is d Suppose that the person has already been waiting for 1 3 minutes Find the probability that the person s total waiting time will be between 3 4 and 3 8 minutes e 79 of all customers wait at least how long for the train minutes

The uniform distribution of a random variable X is given in the figure below 1 2 From the figure what is P X 0 54

A normal distribution has a mean of 126 and a standard deviation of 4 Find the z score for a data value of 119 Round to two decimal places

als Questi ind the critical value z necessa c 0 96

K Assume that the proba one year term life insu

Question A student is taking a standardized each correct answer Questions le question and the student is penal

A pizza chain wants to send codes for 2 off a large pizza to the subscribers of its e mail list Each coupon code will have three letters followed by two digits The letters M N and o and the digits 1 3 5 and 7 will not be used So there are 23 letters and 6 digits that will be used Assume that the letters and digits can be repeated How many such coupon codes can be generated

Solve the given initial value problem y 4y 4y 5 x e 2x y 0 4 y 0 7 2x y x e 4 x 5x 3 X 2 6 X

esting Question 13 7 1 47 Part 1 of 3 Determine whether the claim stated below represent test is performed how should you interpret a decisio null hypothesis A researcher claims that more than 89 of people ha

Suppose we want to choose 5 colors without replacement from 8 distinct colors If necessary consult a list of formulas a How many ways can this be done if the order of the choices does not matter b How many ways can this be done if the order of the choices matters X

Mancini s Pizzeria sells four types of pizza crust Last week the owner tracked the number sold of each type and this is what he found Type of Crust Number Sold Thin crust Thick crust Stuffed crust Pan style 322 230 171 194 Based on this information of the next 3000 pizzas he sells how many should he expect to be thick crust Round your answer to the nearest whole number Do not round any intermediate calculations pizzas X

According to a study conducted in one city 28 of adults in the city have credit card debts of more than 2000 A simple random sample of n 200 adults is obtained from the city Describe the sampling distribution of p the sample proportion of adults who have credit card debts of more than 2000 Round the standard deviation of the sampling distribution to four decimal places OA Binomial p 56 op 6 35 B Approximately normal p 0 28 p 0 0320 C Exactly normal Hp 0 28 p 0 0320 D Approximately normal p 0 28 p 0 0010

The U S housing market estimates that 31 of all homes purchased in 2019 were considered investment properties If a sample of 800 homes sold in 2019 is obtained what is the probability that at most 250 homes are going to be used as investment property Round to four decimal places OA 0 4392 OB 0 5935 OC 0 0934

Determine pand o from the given parameters of the population and the sample size Round the answer to three X decimal places where appropriate 33 o 36 n 36 OA 33 000 1 000 OB 33 000 0 36 000 OC 33 000 0 6 000 OD 5 500 0 6 000

To assess attitudes towards issues that affect the residents of a village the village randomly chose 800 families to participate in a survey of life attitudes The village received 628 completed surveys What is the sample proportion of completed surveys Round to three decimal places OA 0 628 OB 1 274 OC 0 785

are as always subject to the Code of Co seriously on 32 an appropriate response value of E the margin of error for c

Question 34 Provide an appropriate response Suppose you want to test the claim that u H of significance of a 0 01 when should you reje

Question 23 Provide an appropriate response Us ormally distribut

ation are normally distributed with a mean of 138 and a standard deviation of 2 Find the mean and standard error of the mean for this sampling distribution when using random 158 5

Provide an appropriate response Assume that the random variable X is normally distributed with mean 90 and standard deviation 12 Compute the probability P 57 X 105 O 0 7888 0 8819 0 8914 0 8944

Use the standard normal distribution to find P 2 25 z 0

An ordinary fair coin is tossed 3 times Outcomes are thus triples of heads h and tails t which we write hth ttt etc For each outcome let w be the random variable counting the number of tails in each outcome For example if the outcome is hht then N hht 1 Suppose that the random variable x is defined in terms of N as follows X 2N 2N 1 The values of x are given in the table below Outcome ttt hth thh hhh htt hht tht tth Value of X 11 1 1 1 3 1 3 3 Calculate the probabilities P x x of the probability distribution of x First fill in the first row with the values of x Then fill in the appropriate probabilities in the second row Value X of X 0 0 0 0 X S

EV If necessary consult a list of formulas 11 4 0 C 0 4P3 11C4

uestion cientist surveys 30 of the

Question 11 Out of 200 households sampled 94 construct a 95 confidence interva living at home a Give your confidence interval in answers to three decimal places

d Decide whether to reject or fail to reject the

What is the difference between an ordinary opinion and an opinion in argument O An ordinary opinion is your personal view An opinion in argument must be supported by evidence O An ordinary opinion never has value and an opinion in argument always has value O An ordinary opinion must be supported by evidence and an opinion in argument is your personal view An ordinary opinion is the same as an opinion in argument