Question

Find the probability and interpret the results. if​ convenient, use technology to find the probability. during a certain week the mean price of gasoline was ​$2.715 per gallon. a random sample of 32 gas stations is drawn from this population. what is the probability that the mean price for the sample was between ​$2.691 and ​$2.732 that​ week? assume sigmaσequals=​$0.049

Answer 1

From the given question:

$\mu=\ 2.715 \\ \\ \sigma=\ 0.049$

The probability of a normally distributed data between two values (a, b) is given by:

$P(a\ \textless \ \bar{x}\ \textless \ b)=P\left( \frac{b-\mu}{\sigma/\sqrt{n}} \right)-P\left( \frac{a-\mu}{\sigma/\sqrt{n}} \right)$

Thus,

$P(\ 2.691\ \textless \ \bar{x}\ \textless \ \ 2.732)=P\left( \frac{\ 2.732-\ 2.715}{\ 0.049/\sqrt{32}} \right)-P\left( \frac{\ 2.691-\ 2.715}{\ 0.049/\sqrt{32}} \right) \\ \\ =P(1.963)-P(-2.771)=0.97515-0.0028=\bold{0.97235}$