Statistics for Decision-Making Final Exam Summer 2025

Q1 a) Define the following terms (i) Probability, (ii) Sample space. [CLO-1, L-1] 2 b) Explain the concept of the Central Limit Theorem (C.L.T) and state its properties. [CLO-2, L-2] 3 Q2 The following table lists the probability distribution of the number of breakdowns per week for a machine based on past data

a) Demonstrate this probability distribution graphically. [CLO-2, L-2] 2
b) Utilize the above table find the probability that the number of breakdowns for this machine during a given week is i. exactly 7 breakdowns; ii. 0 to 4 breakdowns; iii. more than 1 breakdown; iv. at most 4 breakdown [CLO-3, L-3] 4 Q3 Suppose all 100 employees of a company were asked whether they are in favor of paying high salaries to CEOs of US companies. The following table shows the response of these 100 employees. In Favor Against Male 15 45 Female 4 36
a) Solve the following conditional probability i. P(In Favor | Female) ii. P(Against | Male) iii. P(Male | In Favor) iv. P(Female | Against) [CLO-3, L-3] 6 b) Select whether the events 'Male' and 'Female' are mutually exclusive? [CLO-3, L-3] 1

Q4 A marketing team sends out promotional emails to potential customers. From past data, the probability that a recipient opens the email is 0.4. If the team sends emails to 8 customers. Applying binomial probability distribution, find the probability- a) Exactly 3 customers open the email. [CLO-3, L-3] 2 b) At most 2 customers open the email. [CLO-3, L-3] 2 c) At least 7 customers open the email. [CLO-3, L-3] 2