Summary
Summary TUTORIAL 5 MEMO
- Course
- Institution
- Book
WITH THESE PAST PAPERS YOU ARE GUARANTEED A DISTINCTION WITH LOTS OF PRACTICE!!!!!!!!!!!!
[Show more]
Connected book
Book Title:
Author(s):
- Edition:
- ISBN:
- Edition:
More summaries for
-
STK 120-SEMESTER TEST 1 2022 (MEMO)
-
TUTORIAL 7 MEMO
-
TUTORIAL 8A MEMO
Seller
Follow
thembisilemagudulela
Content preview
STK110 TUT 5 Preparation sheet memo 2023Question 1 is based on the following information:
The number of telephone calls received during any given minute, on a weekday, at an exchange of
the airport has the following probability distribution:
𝑥 𝑓(𝑥) 𝑥𝑓(𝑥) (𝑥 − 𝜇)2 𝑓(𝑥)
0 0.3 0 0.972
1 0.2 0.2 0.128
2 0.2 0.4 0.008
3 0.1 0.3 0.144
4 0.1 0.4 0.484
5 0.1 0.5 1.024
Sum 1.8 2.760
Let: 𝑥 = Number of telephone calls received during any given minute, on a weekday
Hint: Use STAT MODE where necessary
a) Calculate the expected number of telephone calls received during any given minute.
𝐸(𝑥) = 𝜇 = ∑ 𝑥𝑓(𝑥) = 1.8 (column 3 in table)
b) Calculate the variance and standard deviation of 𝑥
𝑉𝑎𝑟(𝑥) = 𝜎 2 = ∑(𝑥 − 𝜇)2 𝑓(𝑥) = 2.76 (column 4 in table)
𝑆𝑡𝑑 𝑑𝑒𝑣(𝑥) = 𝜎 = √2.76 = 1.6613
c) Calculate the probability that more than 1 but at most 4 telephone calls can be received
during any given minute.
𝑃(1 < 𝑥 ≤ 4) = 𝑃(2 ≤ 𝑥 ≤ 4) = 0.2 + 0.1 + 0.1 = 0.4
Question 2 is based on the following information:
Consider the experiment of shooting a bullet at a target three times. A team consists of
three (3) marksmen, each shooting a single bullet at a target. All three shooters were
trained by the same coach and can be assumed to have the same abilities and skills.
For this team, it is known that the probability of getting a bullseye in any one shot is 0.3.
Let 𝑥 = number of successful bullseye hits for the team.
a) List 4 properties in the context of this scenario to explain why the following statement is true:
“This experiment can be modelled using a binomial distribution.”
1. The experiment consists of a fixed number, 3, of identical trials (3 marksmen trained by the same
coach with similar abilities and skills).
2. Each trial results in one of two outcomes: success (hits a bullseye) or failure (miss the bullseye).
3. The probability of success on a single trial is equal to p = 0.3 and remains the same from trial to
trial.
4. The trials are independent. … three different marksmen are shooting at targets and the outcome
of one’s shooting does not influence the outcome for the others
1
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller thembisilemagudulela. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $4.00. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
75759 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now