8. With an American penny, the likelihood of getting H when it is spun on edge is 0.3. If X is the random variable where X (H) = 1, X(T) = −1, find the expected value E(X), the variance, Var(X), and express X in its standard form.

Prospect Z = ($1, 0.30 ; $18, 0.40 ; $25, 0.30) What is the standard deviation of prospect Z? (Note: The answer may not be a whole number; please round to the nearest hundredth) (Note: The numbers may change between questions, so read carefully)

1. Suppose the prices of used cars in the market are normally distributed with a mean of $15,000 and a standard deviation of $7,5000. What is the probability of selecting a car from this market and its priced above $20,000.

At races, your horse, White Rum, has a probability of 1/20 of coming 1st, 1/10 of coming 2nd and a probability of 1⁄4 in coming 3rd. First place pays $5,000 to the winner, second place $4,000 and third place $1,350.Hence, is it worth entering the race if it costs $1050?  Your company plans to invest in a particular project. There is a 40% chance you will lose $3,000, a 45% chance you will break even, and a 15% chance you will make $5,500. Based solely on this information, what should you do?  On 1st Jan 2006, a business had inventory of $19,000. During the month, sales totalled $32,500 and purchases $24,000. On 31st Jan 2006 a fire destroyed some of the inventory. The undamaged goods in inventory were valued at $11,000. The business operates with a standard gross profit margin of 30%. Based on this information, what is the cost of the inventory destroyed in the fire?

Please help me with both the question. Thank you

Is this example also an example of economically rational decision making? “In 2019, I started my small business by selling prints of my photographs. Now it’s temporarily closed. During this time I had the option of shipping my prints through USPS or UPS. I decided to ship my prints through USPS instead of UPS since it was a bit expensive at the time. My prints that were shipped out from USPS arrived in time and came in good condition. The opportunity cost is the cost of UPS shipping.”

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