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

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11-10-2017
Mathematics

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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

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nobillionaireNobley nobillionaireNobley · Answer 1 · 2017-10-18T16:24:33+02:00

From the given question:

[tex]\mu=\$2.715 \\ \\ \sigma=\$0.049[/tex]

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

[tex]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)[/tex]

Thus,

[tex]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}[/tex]