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.
