Summary
Summary STK110-TUTORIAL 7A
- 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 Preparation sheet: TUT 7A memo 2023Question 1
At the end of a rugby match, the game can be extended into injury time. The injury
time that is incurred is uniformly distributed between 0 and 10 minutes.
Let: 𝑥 the amount of injury time in minutes that is incurred at the end of a match.
𝑥̅ the average amount of injury time in minutes that is incurred at the end of a match
for 30 matches.
a. Write down the probability density function of 𝑥
1 1
, 0 𝑥 10
𝑓 𝑥 10 0 10
0, 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒
b. Calculate the probability that a game is extended with injury time between 6 and 8 minutes.
1
𝑃 6 𝑥 8 2 0.2
10
c. The injury time incurred was recorded for 30 matches. Calculate the probability that the average injury
time is between 4 and 6 minutes.
Let 𝑥̅ average injury time (in minutes) incurred at the end of the game
𝑎 𝑏 0 10
𝐸 𝑥 𝜇 5
2 2
𝑏 𝑎 10 0
𝑉𝑎𝑟 𝑥 𝜎 8.333
12 12
𝜎 √8.333 2.8867
4 5 6 5
∴𝑃 4 𝑥̅ 6 𝑃 𝑧 𝑃 1.8975 𝑧 1.8975 𝑃 1.90 𝑧 1.90
2.8867 2.8867
√30 √30
0.9713 0.0287 0.9426
d. Find the probability that the sampling error of 𝑥̅ for a random sample of 30 matches, will be more than
1 minute.
𝑃 |𝑥 𝜇| 1
𝑃 𝑥 𝜇 1 𝑃 𝑥 𝜇 1
𝑥 𝜇 1 𝑥 𝜇 1
𝑃 𝑃
𝜎 0.5270 𝜎 0.5270
𝑃 𝑍 1.90 𝑃 𝑍 1.90 2 0.0287 0.0574
e. What will the 20th percentile of average injury time be?
𝑃 𝜇
𝑃 𝑧 0.84 0.2 ∴ 20 0.84 ∴ 𝑃20 0.84 0.5270 5 ∴𝑃 4.5573
𝜎 𝑋
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