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( (b-\mu)/(\sigma/√(n)) \right)-P\left( (a-\mu)/(\sigma/√(n)) \right)`

Thus,


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