Data Analysis, Probability, and Statistics - HiSet: High School Equivalency Test: Math

Step 1: Find the probability of getting a green marble...

The probability of a green marble is .

Step 2: Find the probability of getting a blue marble (without replacement)

When we have without replacement, we do not put the first marble we take out back into the sack. In this case, the total number of marbles in the sack is less.

Probability of a blue marble is .

Step 3: To find the probability of both events happening at the same time, we need to multiply the probabilities in the first two steps.

So,

Step 4: Simplify...

is the answer.

The mean is found by adding the values in a set and dividing that number by the total number of values.

The mean of a data set is equal to the sum of the terms divided by the number of terms, which here is 9. Therefore,

The median of a data set with an odd number of terms is the term that falls in the middle when the terms are ordered. The terms are already ordered:

so the element that falls in the middle is 12.

The mode of the data set is the term that occurs most frequently, which is 12.

The midrange is the mean of the least and greatest elements, which is

.

Of the four - mean, median, mode, and midrange - the median and the mode are equal.

The mean of a data set is equal to the sum of the terms divided by the number of terms, which here is 9. Therefore,

The median of a data set with an odd number of terms is the term that falls in the middle when the terms are ordered. The terms are already ordered:

so the element that falls in the middle is 12.

The mode of the data set is the term that occurs most frequently, which is 12.

The midrange is the mean of the least and greatest elements, which is

.

Of the four - mean, median, mode, and midrange - the median and the mode tie for being the least.

In order to solve this standard we need to understand two primary components: probabilities and the property of independent events. A probability is generally defined as the chances or likelihood of an event occurring. It is calculated by identifying two components: the event and the sample space. The event is defined as the favorable outcome or success that we wish to observe. On the other hand, the sample space is defined as the set of all possible outcomes for the event. Mathematically we calculate probabilities by dividing the event by the sample space:

An intersection is the likelihood that one event will occur with another.

We can calculate that the probability of rolling a one on a six-sided die is:

Now, let's determine the probability of flipping a coin to reveal the "heads" side. A coin has two sides: heads or tails. The probability of rolling heads is as follows:

An intersection is the probability of two events occurring simultaneously; therefore, we need to multiply the probabilities.

Convert to a percentage.

From the question, we know that 60 out of a random sample of 80 locations experienced increased sales in the last two weeks; however, because this data is only from a random sampling of locations, it is difficult to say anything absolute about the population (all of the locations).

While 75% of the random sample did experience increased sales, we cannot know for certain what portion of the entire population experienced increased sales. What we can conclude from this data is that it is likely that the percentage of restaurants that experienced increased sales is roughly around 75%.

Therefore, the statement that can be made with the most certainty is that "It is very likely that more than half of all franchise locations experienced increased sales in the last two weeks."

From the question, we know the average age from a random sample of 50 people was 28.5 years; however, because this data is only from a random sampling of people, it is difficult to say anything certain about the entire population.

While it seems that the previously reported age is wrong, and that the average age of people on the island is likely around 29, it is impossible to say for certain what the average age actually is without gathering data for every single person on the island.

With findings from a random sample, you can draw conclusions about what is likely.

It is likely that the actual average age is lower than the previously reported average age; however, without data for every single person in the population, statements that are certain, such as, "The average age of the indigenous people on the island is 28.5 years," cannot be made.

Note that the statement, "The average age of indigenous people on the island is between 28 and 29 years," is a certain statement, even though it does not give an exact value for the average. Even though researchers found an average age of 28.5 years, it is still very possible that the actual average age is outside the range of 28 to 29.

Therefore, the statement, "It is very likely that the average age of people on the island is actually much lower than previously reported," is the answer because it does not try to make any certain claims and the conclusion is supported by the findings.

The formula for a regression line for a set of paired data is the line of the equation

,

where

and

.

, the number of pairs.

is the sum of the values:

is the sum of the values:

is the sum of the squares of the values:

is the sum of the products:

Substituting:

and are the arithmetic means of the and values, respectively - the sums divided by the number of values:

The equation of the linear regression line is .

The formula for a regression line for a set of paired data is the line of the equation

,

where

and

.

, the number of pairs.

is the sum of the values:

is the sum of the values:

is the sum of the squares of the values:

is the sum of the products:

Substituting:

and are the arithmetic means of the and values, respectively - the sums divided by the number of values:

The linear regression line is the line of the equation .

On the horizontal axis of a histogram, you have labels representing ranges of values. For example, the label "140–159" represents the range of islands with populations between 140 and 159.

The question asks for the percent of islands with populations under 140. The ranges that are smaller than 140 are the "120–139" range and the "100–119" range. Match the bars of each with the percents on the vertical (y) axis. The percents corresponding to these ranges are 35% and 30%, respectively.

Adding both of these percents yields the answer, 65%.

In a deck of 52 cards, one-fourth of the cards, or 13 cards, are spades. Also, there are four aces, one of which is a spade and three of which are not spades. It follows that the removal of the spades and the aces results in the removal of

cards, to leave a modified deck of

cards.

None of the two red threes (the three of clubs, the three of diamonds) were removed, so the probability of a random draw of a red three is

.

The number of ways to choose four people to sit at the first table without regard to the arrangement at either table is the number of combinations of four people from a set of eight; once the people who will sit at the first table are chosen, the people who will sit at the second are automatically chosen. Therefore, the correct number of such arrangements is .

Since

,

then, setting ,

,

the correct number of arrangements.

Because the last test cannot be either math or writing, the selection of an order in which the tests are taken must be looked at as a sequence of events as follows:

First, the test to be taken last must be one of three tests: reading, science, or social studies;

Second, the remaining four tests must be arranged in a particular order. There are four ways to schedule the first test, three remaining ways to schedule the third, two for the third, and one for the fourth.

By the multiplication principle, this makes

possible schedules.

The question asks for you to find the revenue in the year 2004. The horizontal axis is labeled "Year," so look there first to find where the label for 2004 is.

Tracing upwards, you will see that the value 2004 corresponds to a value of about 16 on the vertical axis. Since the label for the vertical axis is "Dollars in Millions," this means that the revenue in 2004 was 16 million dollars.

In numerical form, 16 million dollars is $16,000,000.

Each bar in this histogram represent the percent of employees with salary in the given range. For example, the bar above the label "150–159" means that 25% of the employees earn between $150,000 and $159,000.

Since we want the percent of employees who earn $180,000 or more, we need to add the values for the bars for "180–189", "190–199", and "200–210".

The bars show that 15% of employees earn between $180,000 and $189,000, 15% earn between $190,000 and $199,000, and 5% earn between $200,000 and $210,000.

Adding these percentages together yields 35%.

The line graph is best used with data that occurs sequentially, especially sequentially over a period of time. The line graph is best at describing a general trend, such as an increase or decrease, over time.

The decrease in weight of an adult male over 12 months fits a line graph well because there is data that can be organized sequentially (chronologically, in this case) and because we would be looking for some sort of trend in the data, a decrease over time in this case.

The question asks you to identify a trend that best fits the data.

Over 10 years, the revenue of the company decreases and increases with no clear overall pattern or trend, so the answers claiming that there is a general increase or decrease are incorrect.

While the revenue was at a high point ($65,000) in the year 1994, it was not the highest point in the 10 years. The highest point was in 1998, with a revenue of $77,000.

While the revenue did increase from 1991 to 1992, it decreased by even more from 1991 to 1993. Therefore, from 1991 to 1993, there was actually a net decrease in revenue, not a net increase.

The correct answer is: "The company's revenue generally decreased from 1994 to 1996." Notice the data points matching the years 1994, 1995, and 1996 are linked by a line that has a downward slope. This indicates a general decrease in revenue.

Notice that the question narrows the time period you are examining to 1994–1998. While there are years with higher incomes than in this time period (namely, 1992 and 1999), we can only consider the years from 1994 to 1998.

The highest point within this period is in the year 1998. Matching this data point with the values on the y-axis (the income values), you will see that this data point lies between $400,000 and $500,000. Looking more closely, you can even say that it is above halfway between the values, so it appears to be greater than $450,000.

Thus, the value that approximates the income in 1998 is $460,000.

Be careful to take into account the units on each axis. The y-axis measures income in thousands of dollars, so the answer is $460,000 and not $460.

In order to solve this problem, we need to discuss probabilities. A probability is generally defined as the chances or likelihood of an event occurring. It is calculated by identifying two components: the event and the sample space. The event is defined as the favorable outcome or success that we wish to observe. On the other hand, the sample space is defined as the set of all possible outcomes for the event. Mathematically we calculate probabilities by dividing the event by the sample space:

The die has six sides with the following values: one tow, three, four, five, and six. Of these values the die has three that are even: two, four, and six. We can write the following probability.

Simplify.

Now, let's convert this into a percentage: