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.
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.