In a large city, 45% of residents use public transport for their daily commute. A random sample of 40 residents is taken. Let the random variable XXX represent the number of residents in the sample who use public transport.
Find (i) P(X=22)P(X = 22)P(X=22) (ii) P(X<15)P(X < 15)P(X<15) (iii) the smallest value of kkk such that P(X≤k)>0.6P(X \le k) > 0.6P(X≤k)>0.6
A new larger random sample of 500 residents is taken.
(i) Using a suitable normal approximation, find the probability that at least 215 of these 500 residents use public transport. (ii) Justify why a normal approximation is appropriate in part (b)(i).
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.