Name:

  1. A day trader buys an option on a stock that will return $100 profit if the stock goes up today and lose $400 if it goes down. If the trader thinks there is a 75% chance that the stock will go up,

    1. What is the expected value of the option’s profit? \(E(x) = -25\)

    2. What is the standard deviation of the option’s profit? \(SD(x) = 216.506\)

    3. What do you think of this option? With a negative expected value and large standard deviation, this option looks to risky for not a lot of reward. Probably not a good investment.

  2. Fifty percent of Americans believed the country was in a recession, even though technically the economy had not shown two straight quarters of negative GDP growth. For a sample of 20 Americans, make the following calculations.

    1. Compute the probability that exactly 12 people believed the country was in a recession. \(0.12\)

    2. Compute the probability that no more than 5 people believed the country was in a recession. \(0.021\)

    3. How many people would you expect to say the country was in a recession? \(10\)

    4. Compute the variance and standard deviation of the number of people who believed the country was in a recession. \(VAR = 5\) and \(SD = 2.236\)

  3. Suppose sales at a car dealership are distributed normally by month with a mean of $98,000 and a standard deviation of $14,000. Answer the following questions.

    1. What is the probability that sales will exceed $112,000? 0.159

    2. What is the probability that sales will be less than $87,000? 0.216

    3. What is the probability that sales will be within plus and minus one standard deviation of the mean? 68.3%

  4. The average return for companies making up the S&P 500 is 8%, and the standard deviation is 12%. Assume stock returns are normally distributed.

    1. What is the probability a company will have a stock return of at least 6%? 0.566

    2. What is the probability a company will have a stock price no higher than 2% 0.309

    3. What stock return would put a company in the top 10% of returns? 23.379

  5. Assume a random variable has a standard normal distribution. Use this information to answer the following questions.

    1. What is the probability \[P(z \geq 1) = 0.159\]

    2. What is the probability that \[P(z \leq 0.5) = 0.691\]

    3. What is the probability that \[P(-1 \leq z \leq 1) = 0.683\]

    4. What is the probability that \[P(-2 \leq z \leq 2) = 0.954\]

    5. What is the probability that \[P(-3 \leq z \leq 3) = 0.997\]

    6. Find the value of Z where \[P(z \leq Z) = 0.6, z = 0.253\]