Computers in Elementary Schools Elementary and secondary...

Computers in Elementary Schools Elementary and secondary schools were classified by the number of computers they had. $$ \begin{array}{l|llllll}{\text { Computers }} & {1-10} & {11-20} & {21-50} & {51-100} & {100+} \\ \hline \text { Schools } & {3170} & {4590} & {16,741} & {23,753} & {34,803}\end{array} $$ Choose one school at random. Find the probability that it has a. 50 or fewer computers b. More than 100 computers c. No more than 20 computers

Computers in Elementary Schools Elementary and secondary schools were classified by the number of computers they had.
$$
\begin{array}{l|llllll}{\text { Computers }} & {1-10} & {11-20} & {21-50} & {51-100} & {100+} \\ \hline \text { Schools } & {3170} & {4590} & {16,741} & {23,753} & {34,803}\end{array}
$$
Choose one school at random. Find the probability that it has
a. 50 or fewer computers
b. More than 100 computers
c. No more than 20 computers

Key Concepts

Random Sampling

Random sampling is the process of selecting a subset of elements from a larger population in such a way that every element has an equal chance of being chosen. This method ensures unbiased and statistically representative results, which is crucial when using frequency distributions and probability calculations to infer properties of the entire population.

Probability

Probability is the measure of the likelihood that an event will occur. It is calculated as the ratio of the number of favorable outcomes to the total number of outcomes in the entire sample space. This concept is essential when determining the chance of selecting a sample that meets specific criteria, such as the number of computers in schools.

Frequency Distribution

A frequency distribution is a summary of how often different values occur within a data set. It organizes data into categories along with their counts, which assists in visualizing and analyzing the spread and central tendencies of the data. This tool is vital for associating probabilities with each discrete category, such as groups of schools by computer counts.

Transcript

00:02 Okay, so for this question, we want to find out the likelihood that if we pick one school from all of these schools, that that school has 50 or less computers.

00:22 So the probability of just choosing one school out of all of these schools is just going to be one over this plus this plus this and so on.

00:34 And that ends up being 83 ,057.

00:45 The next step is that we don't want the probability of just choosing one school.

00:51 We want the probability that if we choose one school, that that school will have less than or equal to 50 computers.

01:04 And here we're just going to call computers c, so you don't have to write it out all the time.

01:10 So the way that we do that is we look at our table here and we say, well, these schools have less than are equal to 50.

01:20 And so does this one and so does this one.

01:25 So what we're going to do, like we did before, we're just going to add up these three schools.

01:34 So that's going to be 3 -170 plus 4590.

01:45 Plus 16, 7, 4, 1.

01:50 And then, because it's, we're trying to figure out from all of these schools, how many fit the criteria that there are less than or equal to 50.

02:04 So that's gonna be these ones, these schools, divided by all of the schools.

02:19 And that's because it's the proportion of all the schools that fit less than are equal to 50 computers.

02:30 So if we add all this up, this becomes 24 ,501, and then we divide that by again the total amount of schools.

02:48 And that will give us a very long number with lots of decimal places and because it's so long, dot, dot, dot, we're just going to round it to make it easier to read.

03:06 So it's a little easier to understand.

03:11 So there we go...

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