Given the various industries we examined (i.e. agriculture, tobacco, banks, pharmaceuticals, etc.), which industries do you suspect have the highest betas? Which ones have the lowest betas? Provide an economic explanation for your reason. Hint: Talk about the business operations of each industry and how demand for their products/services is affected during up- and down-markets.

• In a university, the population mean GPA is 3.0 and the standard deviation of GPAs is 0.72. I’m going to draw samples of size n=100
  • The z-score of a sample average GPA of 2.95 is -0.69444444
  • The z-score of a sample average GPA of 2.8 is ____
  • The z-score of a sample average GPA of 2.9 is ____
  • The z-score of a sample average GPA of 3.15 is ____
  • The z-score of a sample average GPA of 3.25 is ____
  • The probability of getting a sample average GPA of 2.95 or less is 24.37%
  • The probability of getting a sample average GPA of 2.9 or less is _____
  • The probability of getting a sample average GPA of 2.8 or less is _____
  • The probability of getting a sample average GPA of 3.15 or more is _____
  • The probability of getting a sample average GPA of 3.25 or more is _____
  • The probability of getting a sample average GPA between 2.9 and 3.15 is _____
  • The probability of getting a sample average GPA between 2.8 and 3.25 is _____
• What’s the rule of thumb for the sample size to be “large?

STAT_14_3

Ronit has a box with beads. The beads are opaque or transparent and available in several colors.
The probability that a random bead will be red is 0.3. The probability that a bead will be transparent is 0.6.
Of the red beads - the probability of a random bead being transparent is 0.5

A. Remove 8 beads from the box at random and upon return (sampling with replacement). What is the probability that exactly two of them will be red?
B. Take beads out of the box accidentally and on return (sampling with replacement) until you first remove a transparent bead.
1. What is the probability that more than 4 beads will be removed?
2. The first two beads taken out were not transparent. What is the probability of getting 7 beads out of the box?
C. Remove 10 beads from the box at random and upon return (sampling with replacement). What is the probability that exactly three of them will be red and transparent, two opaque and red and 5 transparent and red?

STAT_14_3

Ronit has a box with beads. The beads are opaque or transparent and available in several colors.
The probability that a random bead will be red is 0.3. The probability that a bead will be transparent is 0.6.
Of the red beads - the probability of a random bead being transparent is 0.5

A. Remove 8 beads from the box at random and upon return (sampling with replacement). What is the probability that exactly two of them will be red?
B. Take beads out of the box accidentally and on return (sampling with replacement) until you first remove a transparent bead.
1. What is the probability that more than 4 beads will be removed?
2. The first two beads taken out were not transparent. What is the probability of getting 7 beads out of the box?
C. Remove 10 beads from the box at random and upon return (sampling with replacement). What is the probability that exactly three of them will be red and transparent, two opaque and red and 5 transparent and red?

An engineer is asked to estimate the probability that a hospital will be completely without power during a given period of time. The hospital typically gets its power from the power grid. For the purpose of this problem, assume that power outages causing loss of grid power can be caused by severe weather (probability = 1*10^-2), equipment failure (probability = 5*10^-3), or power demand exceeding supply (probability = 1*10^-3). The hospital also has two backup generators that automatically start when there is a loss of grid power. Each generator can provide enough power for the hospital on its own. Each generator has a probability of not starting of 1*10^-2.

a) Construct a fault tree to represent the hospital being without power based on the assumptions described above.

b) What is the probability that neither generator starts?

c) What is the probability of the hospital being completely without power?

71.

Use the table below to find the probability.

A. If 2 of the 1000 test subjects are randomly selected, find the probability that both had false positive results. Assume that the 2 selections are made without replacement. (Round to 4 decimals)

B.

If 3 of the 1000 test subjects are randomly selected, find the probability that all had false negative results. Assume that the 3 selections are made with replacement. (Round to 9 decimals)

74.

Determine whether a probability distribution is given. If a probability distribution is given, find its mean. (Round to the nearest thousandth). If a probability distribution is not given, state (not a probability distribution). (Check your spelling!)

A machine adjusted to fill 330 ml of beverage has a normal distribution of 330 ml and a standard deviation of 5 ml, which is the average amount of beverage filled into bottles. Amount of beverage filled,
i) If it is below 326 ml, with a probability of 0.03,
ii) 0.002 probability between 326 ml and 332 ml
iii) over 332 ml with a probability of 0.10
the machine will give an error signal.
a) What is the probability that the machine gives an error signal?
b) What is the probability that the machine has filled more than 332 ml of drinks when it is known that it gives a false signal?
c) 8 bottles are selected regardless of these drinks. What is the probability that more than 2 bottles are filled under 325 ml?
d) What is the probability that the average of the beverage amount will be more than 331 ml for another sample of 36 bottles randomly selected from these drinks?

) Quarantine restrictions lift. You’re headed straight to the nearest Irish pub. However, due to the duration of quarantine, you’re socially out of practice, and all you can think about while you’re there is stats! You take a look around and notice that the probability of seeing someone with a beer in their hand is 0.64. The probability of seeing someone drunk is 0.83. The probability of seeing someone drunk, and holding a beer is only 0.60. Finish the following calculations. SHOW WORK!