Summary STK110-TUTORIAL 6

STK110 Preparation sheet: TUT6 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:

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

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

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
Use both your tables and EXCEL to find the answers

Question 5
(i) What is the probability for a random lamp to fail within the first 700 hours.
(ii) What number of lamps might be expected to fail within the first 700 hours?
Question 6
(i) What is the probability for a random lamp to fail between 900 and 1 300 hours?
(ii) What number of lamps might be expected to fail between 900 and 1 300 hours?
Question 7
1% of the lamps burns less than r hours. Calculate r.
Question 8
5% of the lamps burns more than b hours. Calculate b.

Preliminary Memo
Q2 67.5 min
Q3 𝑃(64 < 𝑥 < 66) = 0.2 and 𝑃(69 < 𝑥 < 73) = 0.2
Q4 At most 69 min
Q5 (i) 0.0668 (ii) Approx 134
Q6 (i) 0.6247 (ii) Approx 1249
Q7 Approx 534 hours
Q8 Approx 1328 hours