In: Physics
The number of Ford Trucks sold in a month at a particular dealership varies from month to month. Suppose the probability distribution below describes monthly truck sales at this dealership.
|
x |
f(x) |
|
8 |
0.20 |
|
10 |
0.35 |
|
14 |
0.25 |
|
20 |
0.20 |
a. What is the Expected Value of monthly sales?
b. Calculate the variance and standard deviation of monthly sales.
c. Suppose this dealership makes $1500 profit on each truck sold. What is the expected monthly profit on sales of Ford Trucks?
d. What is the probability that the monthly truck sales at this dealership are at least 10?
In: Statistics and Probability
A carnival game offers a $100 cash prize for a game where the player tries to toss a ring onto one of many pegs. Alex will play the ring toss game five times, with an 8% chance of making any given throw.
What is the probability that Alex tosses one of the five rings onto a peg?
What is the probability that Alex tosses more than one of the five rings onto a peg?
If Alex tossed five rings again and again, how many rings would land on a peg on average, that is, what's the mean number of successes he can expect?
In: Statistics and Probability
There is a special calculator that when adding numbers rounds the number to the closest integer. For example, 1.1 + 2 + 3.6 will be calculated as 1 + 2 + 4. The error from each addition follows a uniform distribution of (-0.5, 0.5).
a. When 1500 numbers are added, what is the probability that the absolute value of the total error is greater than 15?
b. How many numbers can be added until the probability of the absolute value of the total error being less than 10 is equal to 0.9?
Please thoroughly explain where each equation comes from and how to work the problem!
In: Statistics and Probability
1) Calculate the values of the factor "u" and "d".
2) Show a diagram with the binomial development of the price for 3 periods.
3) Calculate theoretically the minimum number of times the stock should go up in order to exercise the call option.
4)Calculate the probability of exercising the call option.
In: Finance
A local scientist surveyed numerous 10m x 10m plots in southern Queensland to investigate the presence of the troublesome invasive species, the cane toad. Alarmingly, she found a mean of 30 cane toads per plot. Under the assumption that the cane toads are randomly distributed and follow a poisson distribution answer the following
(a) What is the expected number of cane toads found per 1m^2 plot?
(b) What is the probability of finding no more than 3 toads in a 1m^2 plot?
(c) What is the probability of finding at least 2 toads in a 1m^2 plot? (3 marks
In: Statistics and Probability
Using diaries for many weeks, a study on the lifestyles of visually impaired students was conducted. The students kept track of many lifestyle variables including how many hours of sleep obtained on a typical day. Researchers found that visually impaired students averaged 9.79 hours of sleep, with a standard deviation of 1.8 hours. Assume that the number of hours of sleep for these visually impaired students is normally distributed.
(a) What is the probability that a visually impaired student gets less than 6.2 hours of sleep?
(b) What is the probability that a visually impaired student gets between 6.9 and 10.22 hours of sleep?
In: Statistics and Probability
A sensor controlled car-robot completes a path maze a couple of
times, learning after each try.
It's success probability is:
P(x)=1- e^-x/2
For the x'th try (x = 1,2,3...) the cars actions are
not dependent on success of previous tries.
A random var R is created - as the outcome of attempted number of
tries.
If a successful event is called '1' ( meaning at least 1) and
failed try is '0' (no success)
i). What is the expectation value for R of the first 2 consecutive
attempts?
ii). What is the probability of success in first 2 consecutive
attempts?
In: Statistics and Probability
A Firm studied the number of lost-time accidents occurring at its plant. Past records show that 7% of the employees suffered lost-time accidents last year. Management assumes that a special safety program will reduce these accidents to 6% in the current year. Also, it estimates that 15% of the employees who had such accidents in the last year will face a lost-time accident in the current year.
a. What is the probability an employee will experience a lost-time accident in both years (to 2 decimals)?
b. What is the probability an employee will experience a lost-time accident over the two-year period (to 2 decimals)
In: Statistics and Probability
Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities. A major hurricane is a hurricane with wind speeds of 111 miles per hour or greater. During the last century, the mean number of major hurricanes to strike a certain country's mainland per year was about 0.56. Find the probability that in a given year (a) exactly one major hurricane will strike the mainland, (b) at most one major hurricane will strike the mainland, and (c) more than one major hurricane will strike the mainland.
In: Statistics and Probability