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'.
390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.