Probability Questions and Answers

A fast food restaurant executive wishes to know how many fast food meals adults eat each week They want to construct a 90 confidence interval for the mean and are assuming that the population standard deviation for the number of fast food meals consumed each week is 1 4 The study found that for a sample of 1271 adults the mean number of fast food meals consumed per week is 3 Construct the desired confidence interval Round your answers to one decimal place Answer How to enter your answer opens in new window 2 Points Inner endpoint Keypad Keyboard Shortcuts

The electric cooperative needs to know the mean household usage of electricity by its non commercial customers in kWh per day They would like the estimate to have a maximum error of 0 15 kWh A previous study found that for an average family the standard deviation is 2 5 kWh and the mean is 15 9 kWh per day If they are using a 85 level of confidence how large of a sample is required to estimate the mean usage of electricity Round your answer up to the next integer

Out of 178 randomly selected adults in the United States who were surveyed 77 exercise on a regular basis Construct a 95 confidence interval for the proportion of all adults in the United States who exercise on a regular basis Round to three decimal places Answer Lower endpoint Upper endpoint Keypad Keyboard Shortcut Tables

The mean per capita income is 23 037 dollars per annum with a variance of 149 769 What is the probability that the sample mean would be less than 23013 dollars if a sample of 134 persons is randomly selected Round your answer to four decimal places Answer How to enter your answer opens in new window 2 Points Keyp

Intelligence Quotient IQ scores are often reported to be normally distributed with 100 0 and 15 0 A random sample of 35 people is taken Step 1 of 2 What is the probability of a random person on the street having an IQ score of less than 95 Round your answer to 4 decimal places if necessa Answer Tables Keybc

The quality control manager at a computer manufacturing company believes that the mean life of a computer is 88 months with a variance of 81 If he is correct what is the probability that the mean of a sample of 84 computers would differ from the population mean by less than 1 39 months Round to four decimal places Answer 2 Tables your answer Keypad

Find the mean of the sampling distribution of sample means using the given information Round to one decimal place if necessary 55 and o 10 n 4 Answer

a normal approximation be used for a sampling distribution of sample means from a population with 53 and 9 when n 64 wer O Yes because the mean is greater than 30 O No because the sample size is more than 30 O No because the standard deviation is too small Yes because the sample size is at least 30 Table

Given the building layout for Store A Store B Store C and Store D what portion of the share 7500 maintenance costs should be apportione to Store D A 2500ft B C D 1250 ft 625 ft 625 ft apportioned cost Round you answer to the nearest hundredth

0 9999451342 5 460398688 x 10 5 Keep working At least one of the answers above is NOT correct Getting things wrong is part of learning 0 9999451342 5 460398688E 05 1 point 456 and standard The Graduate Record Examination is built on the following two distributions the verbal part is normally distributed with mean deviation 120 and the quantitative reasoning part is normally distributed with mean 586 and standard deviation 149 Use this information to compute the following a Compute the score of a student who scored in the 80th percentile on the quantitative reasoning section b Compute the score of a student who scored worse than 70 of the test takers in the verbal reasoning section Keep Working Keep Working Note You can earn partial credit on this pmblem

Several students are unprepared for a multiple choice quiz with 44 questions and all their answers are guesses Each question has four possible answers and only one of them is correct Find the mean number of correct answers for such students

According to the National Student Clearinghouse Research Center women now comprise 60 of enrollment in universities What is the probability in a random sample of 55 university students that more than 35 are women Round your answer to 3 decimal places

In the United States 41 of 18 to 29 year olds said in a survey held in March 2020 that they currently subscribed to Hulu What is the probability in a random sample of 75 18 to 29 year olds that 35 will say they currently have a subscription to Hulu 0 811 0 056 0 103 0 867

According to Gallup 48 9 of the U S are protestant A random sample of 40 U S residents is selected They find that 18 of the residents are protestant Identify n p and x n p X A A

Physicians and pharmacists sometimes fail to inform patients adequately about the proper application of prescription drugs and about the precautions to take in order to avoid potential side effects One method of increasing patients awareness of the problem is for physicians to provide Patient Medication Instruction PMI sheets The American Medical Association however has found that only 25 of the doctors who prescribe drugs frequently distribute PMI sheets to their patients The probability that a randomly selected patient will be hospitalized for a drug related problem given that the person has received the PMI sheet is 32 where as the probability that a randomly selected patient will be hospitalized for a drug related problem given that the person has not received the PMI sheet is 72 A patient is randomly selected Find the probability that the patient received the PMI sheet and was not hospitalized for a drug related problem a 27 31 b 17 100 c 19 50 Od 17 31 e 17 38

Let A and B be two events with P A and BC 1 Find P B Recall that BC denotes the complement of the event B O a 1 Ob 0 75 O c 0 5 Od 0 25 O e 0

Are black defendants in a murder trial more likely to get the death penalty when the victim is white The table below shows the outcome whether the death penalty is imposed or not of murder trials in Florida betwee 1976 and 1987 Death Penalty Imposed Death Penalty not Imposed Defendant White Victim Black Victim White Victim Black Victim 414 16 37 139 White 53 Black 11 0 4 One defendant is selected at random If the selected defendant is black what is the probability that the defendant got the death penalty a 0 028 b 0 0785 c 0 2292 d 0 1135

Horchata 56 Jamaica Carne Al Asada Pastor Totals 0 Tamarindo 7 63 9 6 33 48 Lengua Totals 8 29 12 49 73 35 52 160 The table above lists the preference of tacos and drink combinations for people What s th probability that a person likes horchata or tacos de al pastor You can write your answer a decimal rounded to 4 places or a percent don t include in answer

Find the indicated probability What is the probability that 4 rolls of a fair die will show exactly three fours O 0 0116 0 0039

It is believed that Lake Tahoe Community College LTCC Intermediate Algebra students get less than seven hours of sleep per night on average A survey of 22 LTCC Intermediate Algebra students generated a mean of 7 24 hours with a standard deviation of 1 93 hours At a level of significance of 5 do LTCC Intermediate Algebra students get less than seven hours of sleep per night on average Fill in the blank The Type Il error is not to reject that the mean number of hours of sleep LTCC students get per night is at least seven when in fact the mean number of hours Note at most means less than or equal to at least means greater than or equal to is more than seven hours is at most seven hours is at least seven hours

When a new drug is created the pharmaceutical company must subject it to testing before receiving the necessary permission from the Food and Drug Administration FDA to market the drug Suppose the null hypothesis is the drug is unsafe What is the Type II Error To conclude the drug is safe when in fact it is unsafe Not to conclude the drug is safe when in fact it is safe O To conclude the drug is safe when in fact it is safe O Not to conclude the drug is unsafe when in fact it is unsafe

We want to test if it takes fewer than 45 minutes to teach a lesson plan State the null and alternative hypotheses Match the correct symbol for the null and alternative hypotheses 1 Ho 2 Ha 1 HO 2 Ha 45 45 V Choose Choose

The same Total Station has specified errors of 3mm 2 ppm The instrument was centered over the survey point with an error of 4 mm The error of mis centering the target was 2 mm Compute the estimated error of the mean distance from Point A to Point C from question 8 4 79 mm 3 20 mm 6 18 mm 5 39 mm 10 10 points A level line began on BM1022 elevation 435 45 and closed on BM1231 elevation 418 60 The Plus and minus sights were kept approximately equal Readings in feet listed in the order they were taken are BM 1022 2 12 BS TP 1 12 87 FS 5 69 BS TP 2 4 22 FS 2 36 BS TP 3 8 54 FS 6 25 BS TP 4 7 54 FS 5 91 BS and BM 1231 6 06 FS What is the misclosure of the level run 0 03 1 05 0 07 0 05 1 10 points Compute the adjusted elevation of TP 4 in question 10 118 70 118 74 119 05

Fill in the blanks by converting between percents decimals and fractions give exact answers with all decimals if there is a repeating decimal round to two decimal places Percent Decimal Fraction 0 43 0 19 7 25 1 3

Convert 3 4 to a decimal

Fill in the blanks Fraction 3 8 Decimal Percent 0 25 50

Level 2 office visits are coded at a frequency of 0 26 What percentage of office visits are a Level 2 Do not enter the sign

Convert 0 4 to a percent and simplified fraction Percent Fraction

BONUS Lily frequents 1 of 2 fast food restaurants choosing McDonalds 25 of the time and Burger King 75 of the time Regardless of where she goes she buys French Fries on 60 of her visits Define the following events M Lily chooses McDonalds B Lily chooses Burger King F Lily orders French Fries A THEN P M bu bus ploc dura boos P B SHOW YOUR WORK WHAT WERE YOU THINKING WHEN YOU SOLVED EACH PROBLEM P FM P FB Photos surna din das rod pificadong ruttu WD B The next time Lily goes into a fast food restaurant what is the probability that she goes to McDonalds and orders French Fries That is find P MOF byli Imprud on0 5L older C If Lily goes to a fast food restaurant and orders French Fries what is the probability that she is at Burger King That is find P B F

16 A box contains 1 white 3 blue and 4 silver marbles TWO marbles are randomly selected without replacement Find the indicated probabilities co sull to suport ale show to zaslbisomh sib A Draw the tree diagram that represents the possibilities for the marble selections Write the probabilities along each branch of the tree zos quivoll strons M ablunchM 2980orio pod sonda z 8 in Lionenil 2rebro vdi 4 qui B Are the probabilities for the color of the second marble selected independent of the first selection Explain D What is the probability neither marble is blue C What is the probability both marbles are the same color E What is the probability that the 1st one is silver and the 2nd one is blue TORTY SCOM to local shopping mall were categorized by age and gender as shown 100

s 1 acer tre sa 14 Roll 2 fair dice Each die has 6 faces uede at you A List the sample space choose any technique for this ludy tal rell vil bor B Event A either a 3 or 4 is rolled first followed by an even number Find P A Sal Maups ei songe C Event B the sum of the 2 rolls is at most 7 Find P B D Are A and B mutually exclusive events Yes or No Explain your answer in complete sentences include numerical justification E Are A and B independent events Yes or No bin Explain your answer in complete sentences include numerical justification probabilities AL

17 One hundred shoppers at a local shopping mall were categorized by age and gender as shown in the contingency table below One shopper is selected at random from that group of 100 domins shoppers Shopper Age Groups Gender Under 25 years A1 15 24 39 Male M Female F TOTAL 25 40 years Over 40 years TOTAL A3 12 18 30 1 P A1 3 POM NA1 5 P M A1 7 P Male or 25 40 years old A2 13 18 31 40 60 100 Find the given probability problems below Use the symbolic notation such as A1 Under 25 years old M Male etc 2 P M 4 P A1 M 6 P F UA3

15 A sample space S consists of 5 events with these probabilities P E P E2 2 P E3 3 P E4 P E5 a Find the probabilities for the simple events E4 and Es P E4 b Find the probabilities for these 2 events i M E1 E3 E5 P M ii L E2 Es P L c List the events that are either in event M or event L or both 8 M or L or both P M or L d List the simple events that are in both event M and event L M and L P M and L P Es

Convert Percent Decimal 99 100 to a percent and decimal

Convert to a decimal and a percent 47 20 Decimal Percent

Convert 19 to a decimal and simplified fraction Fraction Decimal

Convert 0 73 to a fraction and percent Fraction Percent

Round 8 9357 to the nearest hundredth

13 Draw 2 cards from a standard 52 card deck with replacement Find the probability of getting at least one black card

12 A student goes to the library Let events B the student checks out a book and D the student checks out a DVD Suppose that P B 0 4 P D 3 and P DB 0 5 a P B b P D and B c P BID e P D B d P D and B

Round using the place value method Fill in the place value chart to aid your work Place 4 654 in the place value chart ones Place 5 941 in the place value chart ones ones tenths hundredths thousandths Place 5 846 in the place value chart ones tenths hundredths thousandths Place 7 753 in the place value chart ones tenths hundredths thousandths tenths hundredths thousandths Place 8 769 in the place value chart tenths hundredths thousandths Round 4 654 to the nearest tenth Round 5 941 to the nearest hundredth Round 5 846 to the nearest whole number Round 7 753 to two decimal places Round 8 769 to one decimal place

Statis 10 A political scientist asked a group of people how they felt about 2 political policy statements Each person was to respond A agree N neutral or D disagree to each of the 2 statements A Describe the sample space that is list all the possible response possibilities to the 2 I have started the list for you statements The sample space is S AA AN B Assuming each response pair in the sample space is equally likely what is the probability that 1 the person agrees with at least one of the 2 statements 2 the person agrees with exactly one of the 2 statements P at least one P exactly one P hoth

Round 16 749 to the nearest thousand

11 Suppose an experiment has outcomes black white red orange yellow green blue and purple where each outcome has an equal chance of occurring Let event C green blue purple and event P red yellow blue Draw a Venn diagram representing this situation

Round to the nearest hundredth 248 942

II True or False 7 T or F An experiment is any activity that results in one and only one of several clearly defined possible outcomes but that does not allow us to tell in advance which of these will happ in any particular instance An event is a collection of one or more outcomes of an experiment The complement of event A consists of all outcomes that are NOT in A 8 T or F 9 T or F Irom U to nt Find the probability of

Round 9 9012 to the nearest tenth

Round 767 to the nearest ten

Round 4 710 to the nearest hundred

Round 5 60503 to the nearest tenth