A survey of 150 employees found that the distance, XXX km, they traveled to work in a day had the following results:
∑x=930and∑x2=7245 \sum x = 930 \quad \text{and} \quad \sum x^2 = 7245 ∑x=930and∑x2=7245Calculate the mean of XXX.
Calculate the standard deviation of XXX.
Assuming that XXX can be modelled by a normal distribution, find: P(5<X<10)P(5 < X < 10)P(5<X<10)
Assuming that XXX can be modelled by a normal distribution, find: P(X=7.5)P(X = 7.5)P(X=7.5)
Determine with a reason whether a normal distribution is suitable to model this data.
It is known that the distance, YYY km, of travel for a different office can be modelled by a normal distribution with standard deviation 3.1. Given that P(Y>15)=0.05P(Y > 15) = 0.05P(Y>15)=0.05, find the value of the mean μ\muμ for this office, correct to three significant figures.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.