Calculation of normal distribution in statistical calculation

Model : CASIO  fx-991MS, CASIO fx-570MS, CASIO  fx-100MS

In statistics often it is necessary to calculate normal distribution.Normal distribution indicates percentage of chance of occurrence of an event based on the observed data.It's one type of probability distribution.

Example: Calculate normalized variate(→t) for x=53 and normal probability distribution P(t) for the following data 55,54,51,55,53,53,54,52.Also calculate Q(t) and R(t) for these data.(Ans: -0.28, 0.387, 0.112, 0.612 respectively)

Some important notes on complex mode and modulas,argument determination

Model : CASIO fx-570MS, CASIO fx-991MS, CASIO  fx-100MS

Note 1: Expression can be stored in CALC memory in complex mode.

Note 2: Variables A,B,C and M can be used in COMPLEX mode. Variables D,E,F,X,Y won't appear in COMPLEX mode.

Note  3: The indicator R↔I in the upper right corner of a calculation result display indicates a complex number result.

Note 4: Direct calculation of (a+ib)ⁿ will show mathematical error.

Example: Compute modulas and argument of the complex number -3+2i. (Ans: 3.606 and 146.31 Degree)

Solution:

(Mode initialization)

How to determine unit vector perpendicular to two coplaner vectors and angle between two vectors

Model : CASIO fx-570MS, CASIO fx-991MS

If you have read the previous post on Determination of Cross Product and Absolute Value of a vector. then determination of angle and unit vector in calculator would be very easy.In order to determine unit vector, cross product of two vector has to be divided with the value of cross product.Again in order to determine angle between two vector, dot product of two vector has to be divided with the value of dot product.The formulas are as follows..

unit vector ẑ = (A*B) / |A*B|
angle θ = (A.B) / AB

How to work with complex numbers in calculator

Model : CASIO fx-570MS, CASIO fx-991MS, CASIO  fx-100MS

The number that has a negative square value is called a complex number. It has a real part and an imaginary part.The imaginary part includes i (=√-1). a+ib is a complex number where a is the real part and ib is the imaginary part.This format is known as rectangular format.Complex numbers are also presented in another format that is known as polar format. r∠θ° is a representation of complex number in polar format.

Example:  Calculate (5+2i)*2∠30°.(Ans: 6.66+8.46i)

Solution:

(Mode initialization)

How to use logical operators in Base Mode

Model : CASIO  fx-991MS, CASIO fx-570MS

Addition,Subtraction,Multiplication, Division are same as arithmetic calculation in Base Mode.Besides this you can use the following logical operators between values in Base-n calculations. The meaning of this operators are as follows..

How to convert decimal number into hexadecimal,binary and octal number.

Model : CASIO  fx-991MS, CASIO fx-570MS
 
Natural number or decimal numbers that we use for our calculation have base 10. There are other format of number like hexadecimal,binary,octal that have base16,2 and 8 respectively. These type of number are often used in programming sector. Base mode of calculator can be used for conversion of such numbers into one another.

Example: Solve (17)₁₀ = (?)₂ = (?)₁₆ = (?)₈.(what is the value of 17 if it is converted in binary (base 2),

How to solve an equation of two degree

Model : CASIO  fx-991MS, CASIO fx-570MS, CASIO  fx-100MS

A two degree equation contains a single variable with maximum power two.it has two roots.It is called quadratic equation. ax²+bx+c=0 is a quadratic equation where x is the variable and a,b,c are constants.This type of equation is solved by a process known as middle term method. But often it's not possible to have the factor. Equation mode of calculator lets you to solve such equations very easily and quickly.

Example: Solve the equation 2x²-3x-1=0.(Ans: 1.78, -0.28)