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Master
of Business Administration (MBA)/ Master of Business Administration (Online)
MBA(OL) / Master of Business
Administration (Banking and Finance) (MBF)/ Master of Business
Administration(Financial Management) (MBAFM)/ Master of Business Administration(Human
Resource Management) (MBAHM)/ Master of Business Administration(Marketing
Management) (MBAMM) Master of Business Administration(Operations Management)
(MBAOM)/Post Graduate Diploma in Operations Management (PGDIOM)
INDIRA
GANDHI NATIONAL OPEN UNIVERSITY
School
of Management Studies
ASSIGNMENT
For
July
2025 and January 2026 Semesters
Course
Code : MMPC-005
Course
Title : Quantitative Analysis for
Managerial Applications
Assignment
Code : MMPC-005/TMA/ JULY/2025
Coverage : All Blocks
Last
date of submission for July 2025 Semester is 31st October, 2025
and
for January 2026 Semester is 30th April, 2026
1.
What is Statistical Decision Theory? Describe the four different states of
decision environment in managerial applications. Which is the most prevalent
state?
Statistical
Decision Theory is a formal framework that integrates statistical methods with
decision making under uncertainty. It provides tools to choose the best action
among alternatives by quantifying the consequences (losses or gains) associated
with each possible outcome and combining these with probabilistic information.
In managerial applications, decision theory helps managers evaluate strategies,
design experiments, set quality control rules,
2. A
certain manufacturing process yields electrical fuses of which, in the long
run, 15% are defective. Find the probability that in a sample of 10 fuses
selected at random there will be:
(a) No defective
(b) At least one defective
Let the number of defective fuses in a sample of size
n = 10 be the binomial random variable X ~ Binomial(n=10, p=0.15), where p =
0.15 is the long-run probability of a fuse being defective. The binomial
probability mass function is:
P(X = k) = C(n, k) p^k (1-p)^(n-k), where C(n,k) is the combination n choose k.
a) No defective (k = 0):
P(X = 0) = C(10,0) (0.
3. A
manager at a drug manufacturing wants to estimate what proportion of the adult
population of India has high blood pressure. He wants to be 99% sure that the
error of his estimate will not exceed 0.02. Census reports indicate that about
0.20 of all adults have high blood pressure. What sample size shall he take?
We use the standard formula for required sample size
for estimating a population proportion with margin of error E and confidence
level corresponding to z. The formula (large-sample approximation) is:
n = (z^2 * p * (1-p)) / E^2
4.
For a set of 1000 observations known to be normally distributed, the mean is
534 cm and SD is 13.5 cm. How many observations are likely to exceed 561 cm?
How many will be between 520.5 and 547.5 cm?
We use properties of the normal distribution. Let X ~
N(μ=534, σ=13.5). For any value x, the standard score (z) is z = (x - μ) / σ.
Using the standard normal distribution table or calculator, we find tail and
interval probabilities, then multiply by total observations (1000) to get
expected counts.
a) Observations exceeding 561 cm:
Compute z = (561 - 534) / 13.5 = 27 / 13.5 = 2.0.
P(X > 561) = P(Z > 2.0) ≈ 0.0228.
5.
Write short notes on any three of the following:
(a) Level of significance
(b) Quartile Deviation
(c) Criterion of optimism
(d) Disproportional Stratified Sampling
(e) Least Square Criterion
(Answer any three)
a) Level of Significance:
The level of significance, denoted by alpha (α), is the probability threshold
used in hypothesis testing to decide whether to reject the null hypothesis.
Common choices are 0.05, 0.01,
b) Quartile Deviation:
Quartile Deviation, also called semi-interquartile range, measures dispersion
based on the
d) Disproportional Stratified Sampling:
In disproportional stratified sampling, the sample size allocated to each
stratum is not in proportion to the stratum's size in the population.
Researchers may oversample small but
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students, get fully solved assignments online
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