STK110 TUT 5 Preparation sheet 2023
Question 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)
0 0.3
1 0.2
2 0.2
3 0.1
4 0.1
5 0.1
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.
b) Calculate the variance and standard deviation of 𝑥
c) Calculate the probability that more than 1 but at most 4 telephone calls can be received during
any given minute.
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.”
b) Develop the probability distribution of 𝑥 by:
(i) Using a tree diagram;
How many experimental outcomes are there?
Calculate the probability of the experimental outcome [S, F, F]
Give the total number of experimental outcomes that will result in 1 success.
(List all experimental outcomes with 1 success (and 2 failures)).
Calculate the probability of exactly 1 success
(ii) The binomial formula (probability mass function);
(iii) Using Excel functions;
(iv) Draw a bar chart of the probability distribution.
c) Determine the probability that the team of 3 marksmen:
(i) will hit at most one bullseye;
(ii) will hit at least one bullseye;
(iii) will hit either 1 or 2 bullseyes;
(iv) will hit 1 and 2 bullseyes;
(v) will miss exactly 2 bullseyes;
(vi) will miss more than 1 bullseyes
d) Calculate the expected number and variance of bullseyes scored
1
Question 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)
0 0.3
1 0.2
2 0.2
3 0.1
4 0.1
5 0.1
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.
b) Calculate the variance and standard deviation of 𝑥
c) Calculate the probability that more than 1 but at most 4 telephone calls can be received during
any given minute.
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.”
b) Develop the probability distribution of 𝑥 by:
(i) Using a tree diagram;
How many experimental outcomes are there?
Calculate the probability of the experimental outcome [S, F, F]
Give the total number of experimental outcomes that will result in 1 success.
(List all experimental outcomes with 1 success (and 2 failures)).
Calculate the probability of exactly 1 success
(ii) The binomial formula (probability mass function);
(iii) Using Excel functions;
(iv) Draw a bar chart of the probability distribution.
c) Determine the probability that the team of 3 marksmen:
(i) will hit at most one bullseye;
(ii) will hit at least one bullseye;
(iii) will hit either 1 or 2 bullseyes;
(iv) will hit 1 and 2 bullseyes;
(v) will miss exactly 2 bullseyes;
(vi) will miss more than 1 bullseyes
d) Calculate the expected number and variance of bullseyes scored
1
