統計與機率
資料分析、機率分佈、假設檢定與統計方法。
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sum that has the highest probability of occurring when two dice are rol…
\(\frac{6}{36}\) (or \(\frac{1}{6}\))
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c. is this game fair? explain your answer. (___ / 2 points) d. what is …
7 ### Part d (Second Sub - Question: Probability of that Sum)
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how do you show division using fractions? study the example problem sho…
1. 1 whole bag(s) 1 one-half bag(s) 2. $1\frac{1}{2}$ bags 3. $\frac{9}{8}$ yards
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2. for each outcome, decide if player 1 wins or if player 2 wins. click…
s (Using Example Assumptions): a. \( \boldsymbol{\frac{1}{2}} \) b. \( \boldsymbol{\frac{1}{2}} \) c. Yes, because the probability of Player 1 winning equals the probability of Pl…
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7. each year, a volunteer organization expects to add 5 more people for…
The explicit formula is \(a_n = 5n+27\) (where \(n\) is the number of years from now, \(n = 1\) for this year) ### Part (b)
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question 8 the article states: \it can be used to manage our water need…
A. renewal or refreshment
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1. the sample space for game b is partially filled out. finish writing …
To complete the sample space, each cell \((\text{Cube 1}, \text{Cube 2})\) is filled with \(\text{Cube 1} + \text{Cube 2}\). Here are the missing values: - **Cube 1 = 2 row**: - (…
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2. answer the questions for game a: a. what is the probability of playe…
No, the game is not fair. Player 1 has a $\frac{1}{4}$ chance of winning, while Player 2 has a $\frac{1}{2}$ chance of winning. Since their winning probabilities are not equal, th…
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2. answer the questions for game a: a. what is the probability of playe…
s: a. \( \frac{1}{4} \) b. \( \frac{1}{2} \) c. \( \frac{1}{4} \) d. No, the game is not fair. Player 1 has a \( \frac{1}{4} \) chance to win, and Player 2 has a \( \frac{1}{2} \)…
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game a start with two coins. each player tosses a coin. - if two heads …
- Tails / Heads: Player 2 wins - Tails / Tails: Play Again
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2. answer the questions for game a: a. what is the probability of playe…
$\frac{1}{4}$ ### Part b
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m2a performance task 3: probability investigation objective use probabi…
- **Sample Space**: The set of all possible outcomes of a random experiment. - **Probability**: A measure of the likelihood of an event occurring, calculated as $\frac{\text{Numbe…
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15 im2a unit 5 test 15. which of these histograms is approximately norm…
A (assuming the first histogram is option A, with the symmetric, bell - shaped distribution of scores)
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14 a pizza shop offers eight different toppings of pizza. grace chooses…
28
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to make lasagna, 4 tablespoons of cheese are needed per serving. what d…
x represents the number of servings y represents the tablespoons of cheese
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13. evaluate \\(\frac{_8c_4}{_8c_5}\\). \\(\frac{_8c_4}{_8c_5} = \\) en…
\(\frac{5}{4}\)
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does this show a proportional relationship between the number of weeks …
No
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12. find the value of $^7p_1$. $^7p_1 = $ enter your next step here
\( 7 \)
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11. five cards have different letters written on them. the letters are …
120 (corresponding to the option with "120")
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is im2a unit 5 test 10. the following spinner is spun and a normal six …
### 10c Explanation (Probability - Conditional Probability) #### Step 1: Define Events Let \( A \) be the event that a 6 was rolled, and \( B \) be the event that the product is g…
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10. the following spinner is spun and a normal six - sided die is rolle…
\(\frac{3}{10}\) (Explanation as above: Using conditional probability, we find the number of favorable outcomes where a 6 was rolled and the product is greater than 10, then divid…
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roy starts with $120 in his bank account. he takes out $15 each week to…
No
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10. the following spinner is spun and a normal six - sided die is rolle…
s: 10c: The probability is \(\boldsymbol{\frac{3}{10}}\) (explanation: Using conditional probability, count favorable (6 rolled, product >10) over total (product >10) outcomes, gi…
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is im2a unit 5 test 10. the following spinner is spun and a normal six …
### 10c: Probability that a 6 was rolled given that the product was greater than 10 #### Step 1: Define the events Let \( A \) be the event that a 6 was rolled, and \( B \) be the…
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weeks, x. number of weeks, x account balance (dollars), y 0 80 1 65 2 5…
$y = 80 - 15x$
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10b what is the probability that the product was a multiple of 4 given …
\(\frac{3}{8}\)
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10. the following spinner is spun and a normal six - sided die is rolle…
\(\frac{1}{2}\)
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10. the following spinner is spun and a normal six - sided die is rolle…
To solve this, we need to fill in the table with the product of the spinner result (1, 2, 4, 6) and the die result (1 - 6). Let's go step by step for each row (die result) and col…
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9. this venn diagram shows the results of a survey identifying what col…
\(\frac{5}{19}\)
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8. a standard six - sided die is rolled. 8a list all the even numbers t…
\(\frac{5}{6}\)
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8. a standard six - sided die is rolled. 8a list all the even numbers t…
2, 3, 5
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8. a standard six - sided die is rolled. 8a list all the even numbers t…
2, 4, 6
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7. students were asked what they are allergic to. the table shows the r…
\(\frac{17}{45}\)
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7. students were asked what they are allergic to. the table shows the r…
\(\frac{1}{3}\) (or the fraction based on the actual table data, e.g., if the table has 9 nut-allergic and 3 both, it would be \(\frac{3}{9} = \frac{1}{3}\); adjust based on the t…
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7. students were asked what they are allergic to. the table shows the r…
\(\frac{13}{45}\) (or approximately \(0.289\))
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7. students were asked what they are allergic to. the table shows the r…
\(\frac{32}{45}\) (or approximately \(0.711\) if a decimal is preferred)
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is im2a unit 5 test 7. students were asked what they are allergic to. t…
\(\frac{2}{5}\)
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7. students were asked what they are allergic to. the table shows the r…
\(\frac{2}{5}\)
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a cake recipe calls for 3 cups of flour for every 1 teaspoon of baking …
For \( x = 0 \), \( y = 0 \); for \( x = 1 \), \( y = 3 \); for \( x = 2 \), \( y = 6 \); for \( x = 3 \), \( y = 9 \). So the completed table (from top to bottom in the "Cups of …
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6. using the venn diagram shown, find: explain probability = \\(\\frac{…
\(\frac{11}{37}\)
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6. using the venn diagram shown, find: 6c ( p(a \text{ or } b) ) probab…
\(\frac{26}{37}\)
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6. using the venn diagram shown, find: 6b ( p(a \text{ and } b) ) proba…
\( \frac{32}{37} \)
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6. using the venn diagram shown, find: probability = \\(\\frac{6}{37}\\…
\(\frac{23}{37}\)
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6. using the venn diagram shown, find: 6a ( p(a \text{ but not } b) ) p…
\(\frac{7}{37}\)
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6. using the venn diagram shown, find: 6a ( p(a) ) probability = enter …
\(\frac{14}{43}\)
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5. miss simpson recorded the hair type and color of her students in the…
| | Red | Brown | Blonde | Black | |----------|-----|-------|--------|-------| | Straight | 1 | 7 | 1 | 7 | | Curly | 1 | 4 | 3 | 2 |
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4. this table describes the departures of cruises out of a port for the…
\(79.7\%\)
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4. this table describes the departures of cruises out of a port for the…
$\frac{21}{46}$ (or $\frac{3}{7}$ or approximately 0.459 depending on data). But since the table is missing, the general formula gives the fraction as $\frac{\text{On - time June}…
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4. this table describes the departures of cruises out of a port for the…
\(\frac{15}{38}\) (or approximately \(0.395\), but the exact fraction depends on the table values. If the table has June on - time = 45, total June = 50, total July = 64, then the…
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4. this table describes the departures of cruises out of a port for the…
To solve part 4b, we need to assume we have the number of cruises that departed on time in June and the total number of cruises in both June and July. Let's assume the following (…
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4. this table describes the departures of cruises out of a port for the…
\(\frac{59}{150}\) (or approximately \(0.39\) or \(39.3\%\) but as a fraction, \(\frac{59}{150}\)) (Note: The answer depends on the actual June data. If the June on - time is diff…
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4. this table describes the departures of cruises out of a port for the…
$20.3\%$
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3. a coin is tossed and lands on heads. will this affect the chances of…
A. No
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2. a single marble is drawn from a jar containing 20 marbles, as shown …
$35\%$
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is im2a unit 5 test 2. a single marble is drawn from a jar containing 2…
30%
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2. a single marble is drawn from a jar containing 20 marbles, as shown …
30%
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1c which event is the most likely to happen? a spinning a 3 or more b s…
A. Spinning a 3 or more
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1b how likely is the event of spinning 15 or more? options: impossible,…
A. Impossible
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read the excerpt from act 5, scene 2, of julius caesar. alarum. enter b…
lack of enthusiasm
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read the excerpt from act 5, scene 1, of julius caesar. octavius. come,…
C. It emphasizes the savagery of the assassins' actions toward Caesar.
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model each scenario. see example 3 21. an amusement park attraction req…
The model for the rider's height \( h \) (in inches) is \( |h - 50| \leq 12 \), and the range of heights is \( 38 \leq h \leq 62 \) inches.
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22. the typical price to see a popular movie in the us is $21.24 and ca…
The price range of a movie ticket is modeled as \( 17.99 \leq x \leq 24.49 \) where \( x \) is the price of a movie ticket.
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no additional details were added for this assignment. show your work th…
5
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a survey asked stamp collectors how many stamps they have in their coll…
The lower fourth of the responses fall between 40 and 60.
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what is the equation of the least squares regression line for the data …
\(y=-0.879x + 43.293\) (the third option)
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read the excerpt from ovid’s \pyramus and thisbe\. and may you, mulberr…
A tree is given symbolic meaning.
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equivalent fractions in higher terms lower terms | \\(\\frac{1}{3}\\)s …
| Lower Terms | Equivalent Fractions in Higher Terms | | | | | | |----|----|----|----|----|----|----| | | $\frac{1}{6}$ | $\frac{1}{4}$ | $\frac{1}{8}$ | $\frac{1}{9}$ | $\frac{1}…
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which are examples of quadrant 1 functions in the ai four - quadrant fr…
- Automated data collection to help marketers - Cleaning floors in stores with no cleaning staff - AI - controlled filling of all the orders in a distribution center
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4 read this line from chapter 5. \i believe i see a damsel in some dist…
1. Figurative language type: Idiom 2. This means: The character sees a woman who appears to be in trouble and goes to help her, using a traditional, widely recognized phrase to de…
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use the unit rate to find the number of cranes adriana can fold in 45 m…
90
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interactive practice: use unit rates to solve problems adriana is foldi…
2
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interactive practice: use unit rates to solve problems tiffany is learn…
45
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interactive practice: use unit rates to solve problems colton lives wit…
80
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1. look at this spinner: which two of these events have an even chance …
A. Spinning an even number, B. Spinning 5 or more
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interactive practice: understand rate concepts mekhi competes in a wint…
bikes
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15. which of the following sets of data is approximately normally distr…
The data set represented by the first histogram (with weight on the x - axis and percentage on the y - axis, showing a symmetric, bell - shaped pattern) is approximately normally …
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14. a teacher wants to select one group of 5 people from his 30 student…
D. 142506
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12. evaluate $^4c_2$. $^4c_2 = $ enter your next step here
\( _4C_2 = 6 \)
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11. find the value of $^6p_3$. $^6p_3 = $ enter your next step here
\( 120 \)
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10. how many different ways can the letters of the word folder be arran…
720
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9. two cards are randomly drawn without replacement from a deck of card…
\(\frac{3}{19}\)
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9. two cards are randomly drawn without replacement from a deck of card…
$\frac{4}{19}$
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9. two cards are randomly drawn without replacement from a deck of card…
\(\frac{9}{19}\)
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8. the diagram shows the decisions of 319 workers choosing to work and …
\(\frac{17}{319}\)
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8. the diagram shows the decisions of 319 workers choosing to work and …
\( P = 1 \) (or in fraction form \(\frac{319}{319}\) which simplifies to 1)
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8. the diagram shows the decisions of 319 workers choosing to work and …
\( \frac{176}{319} \)
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8. the diagram shows the decisions of 319 workers choosing to work and …
Assuming the number of workers who work and not strike is $N$, the probability is $\frac{N}{319}$. If, for example, the number of workers who work is $W$, then $P = \frac{W}{319}$…
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8. the diagram shows the decisions of 319 workers choosing to work and …
\( \dfrac{193}{319} \)
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8. the diagram shows the decisions of 319 workers choosing to work and …
\( \frac{0}{319} = 0 \) (or if there's a different number, but based on the given info, assuming disjoint sets, the probability is 0). Wait, but maybe the diagram shows a differen…
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8. the diagram shows the decisions of 319 workers choosing to work and …
\(\frac{126}{319}\)
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7. a standard six - sided die is rolled. 7a list all the even numbers t…
\(\frac{5}{6}\)
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1) which expression will give a better estimate of 33.1 ÷ 4? 32 ÷ 4 36 …
(Part 1): \(32\div4\)
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which expression will give a better estimate of 48.9 ÷ 5? 45 ÷ 5 50 ÷ 5…
\( 50 \div 5 \) ### Part 2: Estimate the quotient using \( 50 \div 5 \)
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peter drew a scale drawing of a restaurant. the scale of the drawing wa…
18
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7. a standard six - sided die is rolled. 7a list all the even numbers t…
1, 2, 3, 6
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7. a standard six - sided die is rolled. 7a list all the even numbers t…
2, 4, 6
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how many significant figures does the difference 218.7201 - 218.63 cont…
3
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6. using the venn diagram shown, find: 6d ( p(\text{not } b) ) probabil…
\(\frac{10}{43}\) (Note: The actual answer depends on the Venn diagram's details, but based on typical problems and the given \( P(\text{not } B)=\frac{15}{43} \), the answer is l…
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6. using the venn diagram shown, find: probability = \\(\frac{29}{43}\\…
\(\frac{14}{43}\)
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6. using the venn diagram shown, find: probability = \\(\\frac{28}{43}\…
\(\frac{15}{43}\)