Summary STK110-TUTORIAL 6 MEMO

STK110 Preparation sheet: TUT 6 memo 2023

Questions 1 to 4 are based on the following information

Assume the time to fly from Durban to Johannesburg is uniformly
distributed between 65 minutes and 70 minutes.

Let 𝑥 = the time to fly from Durban to Johannesburg




Question 1
The probability density function of 𝑥 is:

1 1
𝑓(𝑥) = {70 − 65 = 5 = 0.2 for 65 ≤ 𝑥 ≤ 70
0 elsewhere

Question 2
The expected time (in min) to fly from Durban to Johannesburg is:


𝑎+𝑏 65+70
𝐸(𝑥) = = = 67.5 minutes
2 2

Question 3
Show that the probability of a flight time of between 64 and 66 minutes is the same as the probability of a
flight time of between 69 and 73 minutes.

𝑃(64 < 𝑥 < 66) = (65 − 64)0 + (66 − 65)(0.2) = 0.2

𝑃(69 < 𝑥 < 73) = (70 − 69)(0.2) + (73 − 70)0 = 0.2


Question 4
In 80% of the time we can expect the flight time to be at most ______69______ minutes.

𝑃(65 < 𝑥 < 𝑎) = 0.8
∴ (𝑎 − 65)0.2 = 0.8
0.8
∴𝑎= + 65 = 69
0.2




Questions 5 to 7 are based on the following information:

A local municipality installs 2 000 electric street lamps in a new housing
development. The life expectancy of these lamps, measured in hours,
follows a normal distribution with a mean of 1 000 hours and a variance
of 40 000.

Let 𝒙 = the life expectancy of these lamps
Also give the Excel function that you will use to calculate the answer.