’n Bloemis maak aflewerings tussen 13:00 en 17:00 daagliks. Aanvaar dat die afleweringstye ’n kontinue uniforme verdeling volg. Die persentasie aflewerings wat na 16:00 gemaak word is / A florist makes deliveries between 13:00 and 17:00 daily. Assume the delivery times follow the continuous uniform distribution. The percentage deliveries which are made after 16:00 is

’n Lugredery beweer ’n vlugtyd van 120 minute tussen Kaapstad en Johannesburg. Veronderstel die vlugtye volg ’n uniforme verdeling tussen 110 minute en 140 minute en dat vliegtuie altyd op die geskeduleerde tyd vertrek. / An airline company claims a flight time of 120 minutes between Cape Town and Johannesburg. Suppose the flight times are uniformly distributed between 110 minutes and 140 minutes and that airplanes always depart on the scheduled time.

 Bereken die waarskynlikheid dat ʼn vlug wat laat aankom, nie meer as vyf minute laat is nie. Neem aan dat ʼn vlug wat langer as 120 minute duur as laat beskou word. / Calculate the probability that the flight that arrives late will be no more than five minutes late. Assume that a flight that takes longer than 120 minutes is considered to be late.

Die verwagte waarde en standaardafwyking van die kontinue uniforme verdeling ( a = 4; b = 11) is / The expected value and standard deviation of the continuous uniform distribution ( a = 4; b = 11) are

Dit word gegee dat X normaal verdeel is met gemiddeld μ = 47.3  en variansie σ² = 36. / It is given that X is normally distributed with mean μ = 47.3 and variance σ² = 36.

Die modus is gelyk aan / The mode equals

Dit word gegee dat X normaal verdeel is met gemiddeld μ = 27.7  en variansie σ² = 25. / It is given that X is normally distributed with mean μ = 27.7 and variance σ² = 25.

Bereken die waarde van die derde kwartiel. / Calculate the value of the third quartile.

Indien X normaal verdeel is met μ = 15 en σ = 3, is P(X = 15) gelyk aan / If X has the normal distribution with μ = 15 and σ = 3, then    P(X = 15) equals

Die datawetenskaplike wat vir 'n aanlyn winkel werk probeer vasstel hoeveel mense die webblad gebruik gedurende 08:00 - 17:00 vir verskillende dae van die week. Sy stel vas dat naweke (Saterdae en Sondae) meer besig as weeksdae is. In die week teken mense op die webblad aan teen 'n gemiddelde koers van 35 mense per uur. Op naweke teken mense op die webblad aan teen 'n gemiddelde koers van 63 mense per uur. Veronderstel u kies 'n dag van die week ewekansig. Wat is die waarskynlikheid dat 37 mense op die webblad tussen 16:00 en 17:00 aanteken? / The data scientist at an online store is trying to determine how many people use the website during 08:00 and 17:00 for different days of the week. She determines that weekends (Saturdays and Sundays) are busier than weekdays. In the week, people sign-on to the website at an average rate of 35 people per hour. On the weekends, people sign-on to the website at an average rate of 63 people per hour. Suppose you randomly select a day of the week. What is the probability that 37 people sign-on to the website between 16:00 and 17:00?

Die tabel hieronder gee die bivariate verdeling van X en Y: / The following table lists the bivariate distribution of X and Y:

Bereken die verwagte waarde van X+Y. / Calculate the expected value of X+Y.

Laat X ‘n diskreet stogastiese veranderlike wees met die volgende waarskynlikheidsverdeling: / Let X be a discrete random variable with the following probability distribution:

Laat Y = 5X. Bereken die variansie van Y. / Define a new variable Y = 5X. Calculate the variance of Y.

Die tabel hieronder gee die bivariate verdeling van X en Y: / The bivariate distribution of X and Y is described here.

Bereken die variansie van X+Y. / Calculate the variance of X+Y.