Those who wish to pursue their engineering in IITs, NITs and other premier institutes in India have to clear the JEE Main and the JEE Advanced exams. Unlike last year, the JEE exam is held in two sessions in 2022. A new committee called JEE Apex Board will conduct the JEE Main and JEE Advanced this year, with the assistance of the National Testing Authority. The exams are expected to be held in June and July. The candidates should prepare wisely to crack the JEE exams.
Statistics is an easy topic to score marks for any engineering exam. Students can expect 2 questions from statistics for the JEE Main exam. In this topic, there are many formulas to learn. Students can easily byheart those and score marks on this topic. Central limit theorem (CLT) has great importance in statistics. It can be applied to different types of probability distributions. In this article, we discuss CLT, formula, applications of CLT, etc.
Statement
The CLT states that whenever a random sample of size n is taken from any distribution with mean and variance, then the sample mean will be approximately normally distributed with means and variance. The higher the value of the sample size implies more approximation to the normal.
The equation is given by Z = (x̄ – μ)/σ/√n. We make the following assumptions for CLT.
- The size of the sample must be large enough.
- While doing the sampling without replacement, the size should never be greater than ten per cent of the whole population.
- The samples must not depend on each other.
- We should draw the samples randomly by obeying the randomization criteria.
We use CLT to determine the mean family income of a nation. It also helps in data analysis.
Steps to solve the CLT problem
The facts regarding the mean, population size, standard deviation, sample size etc., should be determined from the problem. Then we have to draw a graph with the centre as the mean. Use the formula of Z to find the Z score. For CLT problems having greater than (>) symbol, we have to subtract the value of z-score from 0.5. If the question has less than (<) symbol, then we have to add 0.5 to the z-score value. Then convert the decimal value obtained to percentage.
Binomial theorem
When the power of an expansion becomes larger, it becomes difficult to solve it. Here comes the binomial theorem to help us to solve expansions of the form (x+y)n. The number of terms in the expansion will be n+1. The formula is given by (x + y)n = nC0 xn + nC1 xn-1y + nC2 xn-2 y2 + … + nCn yn. We can find the general term using the formula nCr xn-r yr. Using this theorem, we can easily solve problems related to finding the remainder, finding the digits in a number, etc.
Students are required to download previous years’ question papers on statistics so that they can be familiar with the type of problems asked on this topic. Log on to BYJU’S to download formula PDFs, chapte
click here more
