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Mary is deciding whether to book the cheaper flight home from college after her final​ exams, but​ she's unsure when her last exam will be. She thinks there is only a 30​% chance that the exam will be scheduled after the last day she can get a seat on the cheaper flight. If it is and she has to cancel the​ flight, she will lose ​$250. If she can take the cheaper​ flight, she will save ​$150.

​a) If she books the cheaper​ flight, what can she expect to​ gain, on​ average?

b) What is the standard​ deviation?

Respuesta :

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Answer:

a) $30.00

b) $183.30

Step-by-step explanation:

a) The expected value for booking the cheaper flight is given by the amount saved if she can take the flight multiplied by its probability minus the amount lost if she misses the flight multiplied by its probability:

[tex]EV = (1-0.3)*150 -0.3*250\\EV = \$30[/tex]

She can expect to gain $30.

b) The standard deviation is given by:

[tex]SD = \sqrt{(150-30)^2*0.7+(-250-30)^2*0.3} \\SD = \$183.30[/tex]

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