Statistics is useful when calculating probabilities and keeping records. People use quantitative data and numbers to gain proving knowledge about issues. In the IT sector, statistical math is used in different ways. It is used to mine data, analyze images, and understand algorithms in various AI-powered networks. 

Statistics math is part of the topics learned by IT students at various levels of learning. A lot of students fear dealing with math problems but they only need to do more practice. Here are examples of statistical math problems and solutions for IT. 

What are statistics?

Statistics focuses on the manipulation of data to obtain specific values. Students deal with numerical data analysis and computation. Its basics comprise the use of mean, mode, and median to measure central tendencies. It also uses variance and deviation to measure dispersions. 

Statistical math involves applying math knowledge to collect and analyze data to obtain results. 

Types of statistics

The field of statistics comprises two main types.

Inferential statistics

Inferential statistics is used when people want to obtain meaning from collected data. This is usually data that has been collected, summarized, and analyzed. It is often used when testing a hypothesis. It can also be used to test relationships between variables. 

Descriptive statistics

This data is used to describe summarized results using mean or standard deviation. Data is presented using graphs, bars, charts, tables, and other types of formats. The main purpose of descriptive statistics is to describe. 

Statistic math problems can be challenging due to their complexity. However, it is one of the topics covered in college. A student may not understand every detail after a single class lesson. There is a need for more practice by visiting statistics problems with solutions and answers websites. During assignments, a student can get help with statistics problems from college statistics math problems and solutions on PlainMath. It is possible to solve any math problem a student comes across during their time in college education. 

Examples of statistical mathematical problems and solutions

1. A scientist wants to test the sex of 8 unborn fetuses. What is the probability that 2 of the children are boys?

Solution

Each fetus could either be a boy or a girl.

If only two are expected to be boys, the probability will be 

n(S) = 2x2x2x2x2x2x2x2 = 2⁸. 

n(E) = 1x1x2x2x2x2x2x2 =  2⁶

p(E) = n(e)÷n(s) = 2⁶÷2⁸ = 0.25

You can get more ideas and ways to on Math YouTube channels that are specifically for IT students and those who want to gain expertise in this subject.

2. An airplane is installed with two engines that function independently. The probability that engine 1 will fail is 0.1. The probability that engine 2 will fail is 0.1. What is the probability that the two engines will fail during a flight? 

Solution

Assume E is the probability that engine 1 will fail

F is the probability that engine 2 will fail

P will stand for probability

P(E) = 0.1 and P(F) = 0.1

Now compute the probabilities P(E and F) P(E)P(F) = 0.1 X 0.1 = 0.01

3. The table below shows the probability distribution of is starting salary for new employees. Assume starting salary is X and the figures are to the nearest $10,000

X = ×      0         1        2      3        4       5      6       7

P(x)      0.05   0.15   0.22  0.22  0.17  0.10  0.05  0.04

How much starting salary can a new employee expect?

Solution

E(X) = µ = ∑ x_ip(x_i) =

=0 x 0.05+1 x 0.15 +2 x 0.22+3 x 0.22+4 x 0.17+5 x 0.10+6 x 0.05+7 x 0.04 = 3.01

4. A teacher on a campus computed several interview statistics. She noted that out of every 10 interviews, only 4 jobs were offered. If 66 interviews were done, what is the probability that 30 jobs would be offered? Use T1-84, Silver Edition. 

Solution

Assume n = total interviews

P = job offers

n = 66, p = 4 ÷ 10 = 4

p (30 ≤ X) = 1 – P (X≤29)

= 1 – binomialcdf (66,4,29) = 1 – .7829 = .2171

5. In a certain state, 52% of voters are democrats and 48% are republicans. In another state, 47% are democrats and 53% republicans. Using a sample of 100 voters, what is the probability that represents the highest percentage of Democrats in another state?

Solution

Assume the following

P1 = republican voters in state 1

P2 = republican voters in state 2

p1 = sample of Republican voters in state 1

p2 = sample of republican voters in state 2

n1 = total voters in state 1

n2 = total voters in state 2

To get a better figure, the sample size needs to be bigger. 

P1 x n1 = 0.52 x 100 = 52, (1-P1) x n1 = 0.48 x 100 = 48

If you take P2 x n2 = 0.47 x 100 = 47, (1-P2) x n2 = 0.53 x 100 = 53. This is ˃ 10 which confirms the sample size is bigger. 

Now calculate the difference of the proportions as follows:

E(p1-p2) = ˃ P1 – P2 = 0.52 – 0.47 = ˃ 0.05

Calculate the difference in standard deviation

ơd = sqrt {[ (1-P2) x P2 / n2] + [ (1-p1) x P1/n1]}

ơd = sqrt {[ (0.53) x (0.47) / 100] + [ (0.48) x (0.52) / 100]}

ơd = sqrt (0.002491 + 0.002496) = sqrt (0.004987) = 0.0706

Probability needs to be p1< p2

Transform the variable (p1 – p2) < 0

Z (base (p1 –p2) ) = (x – µ (base (p1 –p2) ) / ơd = (0 – 0.05) / 0.0706 = ˃ -0.7082 = 0.24

Conclusion

Statistical math focuses on the collection of data, its description, and analysis. These results in an inference of conclusions based on quantitative data. Statistics mainly relies on probability theory, linear algebra, and differential and integral calculus.  IT students often find it challenging to solve statistical math. However, it required enough practice and help from professionals.