Question

The average gas price in 2013 was $3.34. The probability that a gas price was less than $2.90 was 20%. What would be the standard deviation?

Answer 1

We know that the probability in a normal distribution can be obtained by the z score, the z score is given as:

`Z=(x-\mu)/(\sigma)`

where mu is the mean and sigma is the standard deviation. In this case we have:

`\begin{gathered} P(X<2.9)=0.2 \\ P(Z<(2.9-3.34)/(\sigma))=0.2 \\ P(Z<(-0.44)/(\sigma))=0.2 \end{gathered}`

Now, to have 20% (that is 0.2) we need that the z score to be -0.842, then we have:

`\begin{gathered} -(0.44)/(\sigma)=-0.842 \\ \sigma=(-0.44)/(-0.842) \\ \sigma=0.52256532 \end{gathered}`

Therefore the standard deviation is $0.52