Likelihood
Is the following event likely, unlikely, impossible or certain?
A 500 page book is opened to page 125.
Possible BUT UNLIKELY
there is a 1/500 = 0.2% chance of that happening.
A standard number cube is rolled.
What is the probability of rolling a number greater or equal to 3?
Sample space: 1, 2, 3, 4, 5, 6
Favorable outcomes: 3, 4, 5, 6
Probability: 4/6 = 2/3 = 66%
There is a 75% chance of rain. How can you simulate this probability with a spinner?
Make 4 equal sections, three labeled rain, and one labeled will not rain.
A local ice cream shop is conducting a survey to determine the most popular ice cream flavor in the city. They randomly select 100 customers who visit the shop over the course of the week and ask them about their favorite ice cream flavor.
Identify the population.
All customers of the local ice cream shop
What does Mean Absolute Deviation (MAD) represent?
The average distance from the mean (or center)
Will tell us if the data is consistent or has variability.
Is the following event likely, unlikely, impossible or certain?
Every 7th grade homeroom teacher at VCP has a set of chrome books.
CERTAIN
Ms. Estevis, Ms. Montez, Mr. Chi, Ms. Gutierrez, Ms. Evaristo and Ms. Vlad all have a set of chrome books in their classrooms.
A standard number cube is rolled and a coin is flipped. What is the number possible outcomes?
Extra 50 points: if you name all the outcomes.
Sample 1 = 1, 2, 3, 4, 5, 6
Sample 2 = Heads, Tails
Total outcomes: 6 x 2 = 12 outcomes
H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6
There is a 40% chance that the teacher is going to crash out today. How can you simulate this probability with a bag of papers?
Put ten papers in the bag and label 4 crash out and 6 no crash out. Draw papers from the bag and document the result. Repeat this about 10 times.
A pediatrician claims that 75% of patients who are late to the appointment are sick. To validate this claim, she selected a random sample of 10 patients who are late to their appointment this month but found only 20% were sick. What could she do to get a more accurate estimate?
She is more likely to get a better estimate by sampling 40 patients instead of 10.
The bigger the sample space, the more accurate the data is.
Which MAD is representative to of the following consistent data?
1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 6
A) Higher mean absolute deviation
B) lower mean absolute deviation
Lower mean absolute deviation means that the numbers in the data are closer to each other in value (consistent)
Is the following event likely, unlikely, impossible or certain?
Everyone at school is a walker.
Possible BUT UNLIKELY
It is possible for all students to be walkers, however, that is very unlikely.
At Subway, you can make a sandwich and choose from
breads: whole grain, Italian;
meats: turkey, ham, chicken;
cheeses: cheddar, provolone, pepper jack;
How many different sandwiches can you make?
2 breads x 3 meats x 3 cheese = 18 different combination of sandwiches.
There is a 1/2 chance that Mr. Chi will participate in the talent show. How can we simulate this probability rolling a standard number cube 5 times.
Roll the standard number cube and count the number of times it lands on numbers that are less than 4 / more than 3 / odd /even / etc. Anything that will give you 50%.
Tracy was conducting a study on the height of tennis players in Texas. She collected a random sample of 50 tennis players across the state of Texas. She found the mean height from the sample was 64 inches tall. How should this data be interpreted?
A) the average height of a single tennis team is 64 inches
B) the average height of all tennis players in Texas is 64 inches
C) the average height of all tennis players in the U.S. is 64 inches
B) the average height of all tennis players in Texas is 64 in
The sample is a representation for the population. It is not always 100% certain, but it serves as a representation since it is unrealistic to get the height of all tennis players in Texas.
The mean absolute deviation (MAD) of the following data is 2.3. What does this mean for the MAD?
1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 20, 53
A) higher deviation
B) lower deviation
The higher the deviation, the more spread out the data is. This makes the data to have more variability. Some numbers will be off.
Is the following even likely, unlikely, impossible or certain?
All students in 5th grade have cell phones.
Possible but UNLIKELY
that every single student in the 5th grades owns a cellphone.
The school is allowing you to customize your spirit shirt. You can choose from
sizes: small, medium, large.
graphic: front, back side of your shirt
colors:white, blue
How many different combinations can you make?
3 sizes x 2 graphic front or back x 2 colors = 12 different combinations.
There is a 1/3 = 33% chance of getting snow in Flagstaff. How can this probability be simulated rolling a standard number cube 10 times?
Roll the cube a few times (like 10 times) and count how many times it lands on 1 or 6 (or any two numbers). This will simulate the probability of 2/6 = 1/3 = 33%.
Abraham wanted to conduct study on how many hours 7th graders spend on their computers at home. He sampled 20 random students and asked how many hours they each spent? The median hours spent on the computer was 1.6 hours. Which of the following is true?
A) the median hours of time spent on the computer for a single class in the 7th grade is 1.6 hours
B) the median hours of time spent on the computer for 40 students is 1.6 hours
C) the median hours of time spent on the computer for all students in the 7th grade was 1.6 hours
C) the median hours of time spent on the computer for all students in the 7th grade was 1.6 hours
The sample is a representation of the population. Instead of asking all 100+ students, they sampled 20 to represent the whole.
Kelia and Sophia each collected a sample of 25 students at their school.
Kelia's sample was asked how much time they spend on homework (mean 1.2hrs; MAD 0.6hrs)
Sophia's sample was asked how much time they spend watching tv (mean 2hrs; MAD 1.3hrs)
Whose data has more variability?
Sophia's
The mean absolute deviation is bigger (1.3hrs) than the MAD of hours on homework. This means that the sample is likely to have more numbers of hours that are far apart.
1, 1.2, 1.6, 1.8, 2, 2.4, 2.8, 3, 17, 26
The mean would not be a good measure of center.
All students who go to Vista College Prep homerooms compete in Voyager challenge next Friday.
Likely
There are homerooms that don't get enough SEARCH points but for the most part, all homerooms earn enough and participate. Therefore it is not certain, but likely!
You roll a standard number cube.
What is the probability of rolling an odd number greater or equal to 3?
Sample space: 1, 2, 3, 4, 5, 6
Favorable outcomes: 3, 5
Probability: 2/6 = 33%
You are using a spinner that has three equal parts: 2 red and 1 blue. You are estimating that the probability of landing on red will be 2 out of 3. You have spun the spinner four times and have only landed on red 1 out of the 4 times. What could you do to get a more accurate estimated probability?
I could spin the spinner x more times.
Repeating the experiment over and over will eventually estimate the probability.
Which sample is a representation of the population?
(this question is a screenshot from 13.3 pg 214)
Sample 2 is a fair representation of the population because it is spread out very similarly to the population.
Kelia and Sophia each collected a sample of 25 students at their school.
Kelia's sample was asked how much time they spend on homework (mean 1.2hrs, MAD 0.6hrs)
Sophia's sample was asked how many hours they spend watching tv (mean 2hrs, MAD 1.3hrs)
Whose data has more consistency?
Kelia's
The MAD is lower than the hours watching tv. This means that the hours are more consistent with each other:
1, 1, 1.2, 1.4, 2, 2, 3, 3, 4
The mean would be a good measure center.