MAT 152 - 101R Probability

Jennie makes the first quartile salary for a construction worker. Markos makes the third quartile salary for a receptionist. Who makes more money?

The receptionist

Jennie makes the median salary for a construction worker. Markos makes the median salary for a teacher. Who makes more money? How much more?

Jennie 50000 - 40000 = 10000

Data was collected for 300 fish from the North Atlantic. The length of the fish (in mm) is summarized in the GFDT below. Lengths (mm) Frequency 100 - 103 1 104 - 107 16 108 - 111 71 112 - 115 108 116 - 119 83 120 - 123 18 124 - 127 3 What is the lower class limit for the first class?

Lower Class Limit = 100

If a person is making the minimum salary for a construction worker, they are making more than what percentage of Teachers?

25%

We are going to calculate the standard deviation for the following set of sample data. 2, 4, 6, 10, 14

1) First, calculate the mean. ¯x= 2+4+6+10+14=36/5= 7.2 2) Fill in the table below. Fill in the differences of each data value from the mean, then the squared differences. 3) Calculate the standard deviation. (x-x): (x-x)^2: 2-7.2 = -5.2 (-5.2)^2= 27.04 4-7.2 = -3.2 (-3.2)^2= 10.24 6-7.2 = -1.2 (-1.2)^2= 1.44 10-7.2 = 2.8 (2.8)^2= 7.84 14-7.2 = 6.8 (6.8)^2= 46.24 ∑(x-x)²: sqrt(23.2) = 4.816 = 4.82 92.8/4 = 23.2

Giving a test to a group of students, the grades and genders are summarized below. A B C Total Male 14 13 19 46 Female 12 10 18 40 Total 26 23 37 86 If one student is chosen at random, find the probability that the student was male OR received a grade of "A". (Leave answer to four decimal places.)

46 (Male) + 26 (A's) - 14 = 58/86 = .6744

The highway mileage (mpg) for a sample of 8 different models of a car company can be found below. Find the mean, median, mode, and standard deviation. Round to one decimal place as needed. 19, 22, 26, 28, 29, 31, 33, 33

Mean x^-:27.625 Median: 28.5 Mode: 33 Standard Deviation: 5.1

Consider the data set 6 9 4 5 2 4 4 3 Find the average (mean): Find the median:

Mean: 37/8 = 4.625 Median: 8/2 = 4

n psychology students took a standardized test. The scores are summarized in the GFDT below. Scores Frequency 200 - 219 17 220 - 239 12 240 - 259 20 260 - 279 280 - 299 19 300 - 319 32 The scores are also described in the cumulative table shown below. Scores Frequency less than 220 17 less than 240 29 less than 260 49 less than 280 69 less than 300 88 less than 320 n What is the missing value in the GFDT?

answer = 20 17 17 12 29 20 49 20 69 19 88 32 120 17+12=29 29+20=49 49+20=69 69+19=88

skewed right

is to the left basically opposite day

As shown above, a classic deck of cards is made up of 52 cards, 26 are black, 26 are red. Each color is split into two suits of 13 cards each (clubs and spades are black and hearts and diamonds are red). Each suit is split into 13 individual cards (Ace, 2-10, Jack, Queen, and King). If you select a card at random, what is the probability of getting: 1) A(n) 6 of Heart's? 2) A Diamond or Spade? 3) A number smaller than 5 (counting the ace as a 1)?

1. 1/52 2. 26/52 = 1/2 3. 4/52 = 1/13

Use the spinner below. P(8 or 11)

2/12 = 1/6

Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 17 11 3 31 Female 6 18 9 33 Total 23 29 12 64 If one student is chosen at random, find the probability that the student did NOT get a "B"

23 (A) + 12 (C) = 35/64

Giving a test to a group of students, the grades and genders are summarized below. A B C Total Male 3 7 13 23 Female 2 8 14 24 Total 5 15 27 47 If one student is chosen at random, find the probability that the student was female OR received a grade of "A". (Leave the answer to four decimal places.)

24 + 5 - 2 = 27/47 = .5744

Calculate x (x-bar) for the data shown, to two decimal places x 27.5 20 20.4 14.7 26

27.5 + 20 + 20.4 + 14.7 + 26 = 108.6/5 = 21.72

A group of people were asked if they had run a red light in the last year. 296 responded "yes", and 142 responded "no". Find the probability that if a person is chosen at random, they have run a red light in the last year.

296/438

Calculate the median of the data shown, to two decimal places x 8.4 6.6 3 1.1 11.9

6.6

The following data represents the age of 30 lottery winners. 22 28 32 34 36 36 40 41 42 43 47 51 52 55 56 56 57 60 61 67 67 71 71 72 75 76 79 79 80 80 Complete the frequency distribution for the data.

Age Frequency 20-29 2 30-39 4 40-49 5 50-59 6 60-69 4 70-79 7 80-89 2

Which of the following statements are true about the boxplot shown here? I. The distribution is skewed right. II. The interquartile range is about 8. III. The median is about 10.

II. The interquartile range is about 8. IQR: Q3 - Q1 = 18 - 10 = 8. The box-plot was skewed to the left.

Here is a FDT for a small data set: data freq 47 3 48 3 49 2 50 3 51 9 Find the following measures of central tendency.

Mean = 47(3)+48(3)+49(2)+50(3)+51(9) = 992/20 = 49.6 Median = 100/2=50 Mode = 51

The following refer to the following data set: 97.2 84.8 116 116 76.5 116 90.8 96.6 101 84.1 What is the arithmetic mean of this data set? What is the median of this data set? What is the mode of this data set?

Mean = 979/10 = 97.9 Median = 97.2 + 96.6 = 193.8/2 = 96.9 Mode = 116

Every year, the students at a school are given a musical aptitude test that rates them from 0 (no musical aptitude) to 5 (high musical aptitude). This year's results were: Aptitude Score 0 1 2 3 4 5 Frequency 2 2 2 3 1 7 The average (mean) aptitude score: The median aptitude score:

Mean: 0+0+1+1+2+2+3+3+3+4+5+5+5+5+5+5+5+5 = 54/17 = 3.176 Median = 3

The boxplot below shows salaries for Actuaries and CPAs. Derek makes the minimum salary for an Actuary. Michael makes the median salary for a CPA. Who makes more money? How much more?

Michael 20,000

Using your calculator, find the range and standard deviation, round to two decimals places: The table below gives the number of hours spent watching TV last week by a sample of 24 children. 50 64 60 56 32 43 89 87 67 45 62 71 24 29 33 47 77 30 65 39 63 60 95 16

Range: 95-16 = 79 Standard Deviation (Sx) = 21.25 STAT - EDIT - Enter data in L1 - STAT - CALC 1 - 2nd 1 - ENTER

Ages Number of students 15-18 10 19-22 10 23-26 5 27-30 7 31-34 7 35-38 8 Based on the frequency distribution above, find the relative frequency for the class with lower class limit 35

Relative Frequency = 10+10+5+7+7+8 = 47= 8/47 = 17%

A sample was done, collecting the data below. Calculate the standard deviation, to one decimal place. x 2 6 16 8 26

Sx = 9.5

Data was collected for 300 fish from the North Atlantic. The length of the fish (in mm) is summarized in the GFDT below. Lengths (mm) Frequency 120 - 129 1 130 - 139 16 140 - 149 71 150 - 159 108 160 - 169 83 170 - 179 18 180 - 189 3 What is the upper class limit for the sixth class?

Upper Class Limit = 179

The highway mileage (mpg) for a sample of 8 different models of a car company can be found below. Find the 5-number summary and use it to create a boxplot. 17, 20, 23, 26, 29, 33, 36, 36

*Enter data into the list editor (Pres STAT 1:EDIT). If you need to clear the list, arrow up to the name L1, press CLEAR, and then arrow down. Put the data values into the list L1. Press STAT and arrow to CALC. Press 1:1-VarStats. Enter L1. Press ENTER. Use the down and up arrow keys to scroll.* Minimum: 17 Maximum: 36 Q1: 21.5 Q2 (Median): 27.5 Q3: 34.5 Q1: 20 + 23 = 43/2 = 21.5 Q2: 29 + 26 = 55/2 = 27.5 Q3: 36 + 33 = 69/2 = 34.5

On a 8 question multiple-choice test, where each question has 2 answers, what would be the probability of getting at least one question wrong?

1 - (1/2)^8 = 255/256

A bag of M&M's has 3 red, 8 green, 2 blue, and 7 yellow M&M's. What is the probability of randomly picking (give answer as a reduced fraction): 1) a yellow? 2) a blue or green? 3) an orange?

1) 7/20 2) 1/2 3) 0

The table below shows the number of deaths in the U.S. in a year due to a variety of causes. For these questions, assume these values are not changing from year to year, and that the population of the United States is 312 million people. Cause Deaths Passenger car occupant 13,100 Motorcycle driver 4,500 Tornado 553 Skydiving 56 a) What is the probability that an American chosen at random died as a passenger car occupant last year? c) What is the probability that you will die as a passenger car occupant next year?

a) 13100/312000000 c) 13100/312000000

A jar contains 8 red marbles numbered 1 to 8 and 10 blue marbles numbered 1 to 10. A marble is drawn at random from the jar. Find the probability of the given event. (a) The marble is red (b) The marble is odd-numbered (c) The marble is red or odd-numbered (d) The marble is blue and even-numbered

a) 8/18 b) 9/18 c) 13/18 d) 5/18

A jar contains 4 red marbles numbered 1 to 4 and 8 blue marbles numbered 1 to 8. A marble is drawn at random from the jar. Find the probability of the given event. (a) The marble is red: (b) The marble is odd-numbered: (c) The marble is red or odd-numbered: (d) The marble is blue and even-numbered:

a) P(R) = 4/12 = 1/3 b) P(Odd) = 6/12 = 1/2 c) P(R|Odd) = 8/12 = 2/3 d) P(B|Even) = 4/12

A jar contains 3 red marbles, numbered 1 to 3, and 9 blue marbles numbered 1 to 9. a) A marble is chosen at random. If you're told the marble is red, what is the probability that it has the number 2 on it? b) The first marble is replaced, and another marble is chosen at random. If you're told the marble has the number 5 on it, what is the probability the marble is red?

a.) 1/3 b.) 1/2

A store gathers some demographic information from their customers. The following chart summarizes the age-related information they collected: Age Number of Customers <20 65 20-30 98 30-40 92 40-50 62 50-60 73 ≥60 75 One customer is chosen at random for a prize giveaway. What is the probability that the customer is at least 30 but no older than 50? What is the probability that the customer is either older than 60 or younger than 30? What is the probability that the customer is at least 50?

a.) 92 + 62 = 154/465 b.) 75 + 98 = 173/465 c.) d.) 75 + 65 = 140/465

Data was collected for a sample of organic snacks. The amount of sugar (in mg) in each snack is summarized in the histogram below. What is the sample size for this data set?

n = 2+3+9+14+11+4+2 = 45

50 psychology students took a standardized test. The scores are summarized in the GFDT below. Scores Frequency 200 - 209 11 210 - 219 11 220 - 229 11 230 - 239 6 240 - 249 11 You would like to build a relative frequency distribution for this data set to easily compare it to another class of students. What is the relative fequency for the second class, 210 - 219? Enter answer as a percent (but do not include the percent symbol).

relative frequency = 11/50 = 22%