CMI 2024 | Data Science | Part B | Question: 20

Question

In June $2017$, a cyberattack named NotPetya spread all over the world. Big companies like Marex, Merck, and FedEx's TNT Express lost a lot of money because of this attack.

Company	Pre-attack Average Monthly Revenue (USD million)	Post-Attack Average Monthly Revenue (USD million)
Marex	$1000$	$700$
Merc	$800$	$480$
TNT Expanse	$500$	$250$

 

Table 1: Financial impact of NotPetya attack on three major companies

Assuming the monthly revenue of Marex follows a Gaussian distribution with a standard deviation of $75$, $(i)$ what is the probability that Marex's revenue will be less than $\$ 850$ million in the pre-attack scenario, and (ii) what is the probability that Marex's revenue will be more than $\$ 850$ million in the post-attack scenario?

$z$	$P(Z \leq z)$
$-2$	$0.0227$
$-1$	$0.1586$
$0$	$0.5000$
$1$	$0.8413$
$2$	$0.9772$

 

Table 2: Note that $Z \sim N(0,1)$

Answer 1

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Workflow of solving Nomral Distribution:

Step1: Assume X={which is required}

Step2: Convert X into Z

Step3: Use Symmetry concept of Z being Even function

Step4: use Given Values and solve for answer

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Part1:

X= {Marex's revenue in PRE-attack scenario)

mean=1000, Standard devaition=75

P(X<850)=?

 

by Step2: Converting X into z

z=(X-mean)/standard deviation

z=(850-1000/)75

z= -2

P(Z< (-2) ) = Given in the question itself = 0.0227

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Part2:

SO we have already taken x for simplicity I am taking y you can any any random variable you want

y= {Marex's revenue in post-attack scenario)

y ~ N{ 700 , (75^2) }

 

P(y>850)=?

 

Step2: converting to z , z=(850-700) / 75 = +2

P (Z>2) = 1 - P(Z<2)

=1 - 0.9772

=0.0228

 

so ans are 0.0227,0.0228