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 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
b. Calculate the probability that a game is extended with injury time between 6 and 8 minutes.
c. The injury time incurred was recorded for 30 matches. Calculate the probability that the average injury
time is between 4 and 6 minutes.
d. Find the probability that the sampling error of 𝑥̅ for a random sample of 30 matches will be more than 1
minute.
e. What will the 20th percentile of average injury time be?
Question 2
A claim has been made that the optimal playing age for a rugby player is 27 years.
After this age, their playing abilities will start to
Let 𝑥 = age of a rugby player (in years) deteriorate.
Suppose that the ages of rugby players are normally distributed with a mean of
25.9 years and standard deviation of 1.54 years.
𝑥̅ = average age for a sample of rugby players (in years)
a. What is the probability that the age of a randomly selected player will be less than the optimal age of 27
years?
b. What must a player’s age be for his age to be in the top 1% of all player’s ages?
c. Find the standard error for a random sample of 25 players if the population average optimal
playing age, 𝜇, is estimated by the sample mean 𝑥̅ ?
d. What is the probability that the average age for a sample of 25 randomly selected players will be more
than the optimal age of 27 years?
e. What is the minimum average age for a sample of 30 randomly selected players to be in the upper
10%?
Preliminary Memo
Q1b 0.2 Q2a 0.7611
Q1c 0.9426 Q2b 29.49
Q1d 0.0574 Q2c 0.308
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 $3.98. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
72042 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now