A telecommunications engineer monitors the reliability of a satellite link. Under specific atmospheric conditions, the probability of a data packet being lost during transmission is 0.15.
State two assumptions required to model the number of packets lost in a sequence of n n\,n transmissions using a binomial distribution.
Using this model, find the probability that exactly 4 packets are lost in a random sequence of 18 transmissions.
Calculate the mean and the variance of the number of packets lost in a sequence of 160 transmissions.
A link is classified as 'unstable' if more than 30 packets are lost in a sequence of 160 transmissions.
Using a suitable approximation, find the probability that the link will be classified as 'unstable'.
67 exam-style questions on OCR A Level Maths 2.4.4 Mean and variance of the binomial (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.