1.A contractor has recently agreed to a project for which it isguaranteed to receive a $100,000 payment.

Additionally, under the terms of the agreement:

• thecontractor must pay a $40,000 penalty if the project requires more than 16 weeks
• the contractor will be paid a $10,000 bonus if the project is completed within 8 weeks.
• There will be no additional payments or penalties for any other outcomes.

The probability that the project will require more than 16 weeks is 0.2 and the probability that the project will be completed within8 weeks is 0.3.

At the end of the project, how much money should the contractorexpectto receivein total?

$ ___________

2. You have just purchased 4 items from a pawn store.

When you returned home, you watched a news report in which acity law-enforcement official statedthat 20% of items sold by pawn shops within the city have been stolen.

If X = the number of items among your purchase that have been stolen, calculate the following probabilities:

P(X = 0) =____________

P(X > 2) =_____________

P(1<X<3) =________________

P(X<2) =_________________

3.Alan, an outdoor aficionado and statistician with an unreasonable fascination with data, always carries an outdoor survival flashlight.

Alan knows that batteries are a critical component of a flashlight, so he conducted extensive research into various battery manufacturers' production data. In the end, he selected a battery that had an average lifetime - in continuous use - of 8 hours, with a standard deviation of 2 hours. Further, he discovered that battery lifetimes in this type of application are approximately normally distributed [i.e. close enough for this problem...].

Alan takes his trusty survival flashlight on a fishing trip.However, Alan has a horrible sense of direction and soon becomes lost on the large lake near his camp. At 9pm, Alan turns on his survival flashlight and shines it in the air, hoping that someone will see his signal and rescue him.

Unfortunately, the search and rescue team did not begin their flight over the lake until 3am the next morning, 6 hours later.If Alan's light is still shining as the search and rescue team becomes airborne, they will easily spot it.

What is the probability that Alan's battery life will be at least 6 hours?_______________

Accepted characters: numbers, decimal point markers, sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation).NOTE:For scientific notation, a period MUST be used as the decimal point marker.

Complex numbers should be in the form {a + bi} where "a" and "b" need to have explicitly stated values.For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Note: Do not use commas. Show all work.

Final answers that include decimal places should be written out to 3 decimals places,after rounding. For example, if your final answer is 7.1234, then enter 7.123. If your answer is 0.1235, then enter 0.124