Question

1a) Suppose you flip a weighted coin 19 times with probability of heads 0.55. Let X equal the number of heads. What is the mean number of heads (to two decimal places)?

1b) Suppose we have weighted coin with probability of heads being 0.30. What is the probability of getting four heads in five flips, to 2 decimal places?   

2) Suppose a particular stock follows the "random walk" model where on any given day there is a 0.02 chance that the stock will go up. If the closing price of the stock doesn't affect the next day's behaviour, and you monitor the stock for ten consecutive days, what is the probability that the stock will increase on between 4 and 6 days (to two decimal places)?

3) You throw darts at a board until you hit the center area. Your probability of hitting the center area is p=0.5. What is the standard deviation of the distribution for the number of throws until you hit the center? (Enter your answer in decimal form to two decimal places.)

4a) Suppose that a romp of otters is normally distributed with mean 9.07 and standard deviation 1.39.

Calculate the size of a romp of otters with a z-score of -0.18, correct to two decimal places.

4b) Suppose that a romp of otters is normally distributed with mean 7.25 and standard deviation 1.61.

Calculate the z-score for a romp of otters of size 8 correct to two decimal places.

4c) Suppose you are interested in the number of lightning fatalities in Canada. You find that there are an average of 8 fatalities per year due to lightning.

What is the probability that there is exactly 8 lightning strikes this year (to two decimal places)?

4d) Suppose you are interested in the number of lightning fatalities in Canada. You find that there are an average of 14 fatalities per year due to lightning.

What is the probability that there is 9 to 11 lightning strikes this year (to two decimal places)?

5a) The amount of time (in minutes) that you wait at the for the crosswalk to turn green is anywhere from 1 to 45 seconds. What is the probability that you wait between 15 and 37 seconds? (Write your answer in decimal form to four decimal places.)

5b) The amount of time (in minutes) that you wait at the for the crosswalk to turn green is anywhere from 5 to 59 seconds. What is the standard deviation (in seconds) for the distribution of the amount of time that you wait for the light to turn green? (Write your answer in decimal form to two decimal places.)

Answer 1