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'.
616 exam-style questions on Edexcel A Level Maths The Normal Distribution, covering 3.1 The Normal Distribution, 3.2 Finding Probabilities for Normal Distributions, 3.3 The Inverse Normal Distribution Function, 3.4 The Standard Normal Distribution, 3.5 Finding the mean and standard deviation, 3.6 Approximating a Binomial Distribution, and 3.7 Hypothesis Testing with the Normal Distribution. Each one has a worked solution and a mark scheme showing where the marks go.