Search & Filtering
Read and analyze the following situations and supply the values of the following variables (if
there is any). On the third column, write known on the space provided if the situation gives
or can compute the value of the variance, otherwise write unknown. Identify also the formula
to be used to estimate the standard error of the mean by writing the symbols or when the
population variance is known and sx when the population variance is unknown.
Situation:
Given the population mean of 12, and a sample
standard deviation of 3 in a sample size of 125
Given:
n=
m=
s=
Answer:
Standard Error Formula:
Consider an electric circuit with an inductance of 0.05 henry, a resistance of 20 ohms, a condenser of capacitance of 100 micro farads and an E = 100 volts. Find I and Q given the initial conditions Q = 0, I = 0 at t = 0
Problem 1:
Soft drinks are put into bottles that hold a nominal 200 ml, but the filling machine introduces a standard deviation of 10 ml. These bottles are packed into cartons of 25 and exported to a market which insists that the mean weight of a carton is at least the quantity specified by the manufacturer. To make sure this happens, the bottler sets the machine to fill bottles to 205 ml. What is the probability that a carton chosen at random fails the quantity test?
Problem 2:
A machine produces parts that have a standard deviation in length of 1.4 cm. A random sample of 100 parts has a mean length of 80 cm. What is the 95% confidence interval for the mean length of all parts?
Problem 3:
MLP Mail-order collects a random sample of 40 customer orders, as shown in the table. What is the 95% confidence interval for the population mean?
The table mentioned below shows the “Gross Production of Energy by Two Sources in India from 2010-11 to 2015-16”. Adopt Exponential Smoothing Method. Consider the Alpha (α) values 0.2, 0.5, 0.7 and find out the one that is comparatively good for the prediction Forecast the value for year 2016-17. Year Coal - (Million Tones) Lignite - (Million Tones) 2010-11 532.7 37.73 2011-12 539.95 42.33 2012-13 556.4 46.45 2013-14 565.77 44.27 2014-15 609.18 48.27 2015-16 639.23 43.84 Source: Open Government Data (OGD) Platform India
7. Express these system specifications using the proposi tions p "The message is scanned for viruses" and "The message was sent from an unknown system together with logical connectives (including negations).
a) "The message is scanned for viruses whenever the message was sent from an unknown system." b) "The message was sent from an unknown system but
it was not scanned for viruses. c) "It is necessary to scan the message for viruses when ever it was sent from an unknown system.
d) "When a message is not sent from an unknown system
it is not scanned for viruses.
7. Express these system specifications using the proposi tions p "The message is scanned for viruses" and "The message was sent from an unknown system together with logical connectives (including negations).
a) "The message is scanned for viruses whenever the message was sent from an unknown system." b) "The message was sent from an unknown system but
it was not scanned for viruses. c) "It is necessary to scan the message for viruses when ever it was sent from an unknown system.
d) "When a message is not sent from an unknown system
it is not scanned for viruses.
ACTIVITY IN BASIC CALCULUS
BASIC RULES IN DERIVATIVE
Complete the blanks of the given function below with a number (except 0 and 1) to create your own problem and find the derivative of the function. Show your complete solution to each problem.
1. f(x) = -4x5 + ______x-4- 2468
2. f (x) =____x-3- _____x1/4 - 12x
3.f(x)= ____ "\\sqrt[4]{x}" 3 - "\\underset{x^6}{=}" + "\\frac{2}{3}" x6
4.f (x) = "\\underset{x^-6}{=}" - ____x2 + "\\sqrt[4]{x}"
Differentiate the following functions:
1.y=1/2(3x^2+1)^2
2.y=3+4x-x^2
Find the derivative of the following
1.y=√x^2-2/2x^3+1
2.y=x^2√6x^2/3x
3.y=2x^2√x
Evaluate the following integrals
(1) integral of {(10x^9+40x^4+3)√(x^10+8x^5+3x+5)} DX
(2) integral of {1/[(x-5)(x^2+4)]} dx
Write whether the following data are discrete or continuous give reason on support of your answer
(1) waiting time of metro when a person reaches metro station
(2)Number of pages in each of the 50 books having some mistakes
(3) Height of students of IGNOU who enrolled in 2021
(4) Number of children in a family in a colony of 100 families
