Among the 120 applicants for a job, only 80 are qualified. If 5 of these applicants are randomly selected for an interview, answer the following:
a. Identify the random process
b. Define a variable
c. Associate the random variable with a distribution and its parameters
Solve using Rstudio:
d. Find the probability that exactly 2 of the 5 are qualified
for the job
e. Find the probability that at least 3 of the 5 are qualified for
the job
f. Find the probability that at most 4 of the 5 are qualified for
the job.
In: Statistics and Probability
According to a local business research, the hourly wage of workers in NY state follows a normal distribution with a standard deviation of $5.00, and a mean $23.00.
What is the probability that a randomly selected NY resident has an hourly wage greater than $25.00?
What is the probability that the average of 6 randomly selected NY residents is greater than $25.00?
What is the probability that all of the 6 people in the randomly selected sample have an hourly wage greater than $25.00?
In: Statistics and Probability
In: Statistics and Probability
Suppose you shuffle a deck of cards and set it down on the table. (a) What is the probability that the top ten cards contain no aces? (There are four aces in the whole deck). (b) What is the probability that the top four cards are all the same suit? (There are four suits, and thirteen cards belonging to each suit). (c) What is the probability that the top four cards contain (exactly one) pair of the same card? (There are thirteen different cards and each occurs four times).
In: Statistics and Probability
The distribution ages for students at Columbia University has a mean of m = 22 and a standard deviation of s = 4. Assume the distribution is normal.
a) What is the probability of selecting a random sample of n = 16 with an average age greater than 23?
b) What is the probability of selecting a random sample of n = 16 with an average age of less than 20?
c) What is the probability of selecting a random sample of n = 16 with an average age is between 19 and 23
In: Statistics and Probability
A 2005 Gallup Poll found that 7% of teenagers (ages 13 to 17)
suffer from arachnophobia and are extremely afraid of spiders. At a
summer camp there are 12 teenagers sleeping in each tent. Assume
that these 12 teenagers are independent of each other.
(a) Calculate the probability that at least 4 of them suffers from
arachnophobia.
(b) Calculate the probability that exactly 4 of them suffer from
arachnophobia.
(c) Calculate the probability that at most 11 of them suffers from
arachnophobia.
In: Statistics and Probability
The distribution ages for students at Western University has a mean of m = 22 and a standard deviation of s = 4. Assume the distribution is normal.
a) What is the probability of selecting a random sample of n = 16 with an average age greater than 23?
b) What is the probability of selecting a random sample of n = 16 with an average age of less than 20?
c) What is the probability of selecting a random sample of n = 16 with an average age is between 19 and 23?
In: Statistics and Probability
An urn contains five red balls, six white balls, and seven blue balls, and a sample of five balls is drawn at random without replacement.
(a) What is the size of the sample space?
(b) Compute the probability that the sample contains three red balls, one white ball and one blue ball.
(c) Compute the probability that the sample contains at least one ball of each color.
(d) Compute the probability that all of the balls in the sample are the same color.
In: Statistics and Probability
Suppose the weights of Farmer Carl's potatoes are normally distributed with a mean of 8.5 ounces and a standard deviation of 0.8 ounces. Round your answers to 4 decimal places.
(a) If one potato is randomly selected, find the probability
that it weighs less than 7 ounces.
(b) If one potato is randomly selected, find the probability that
it weighs more than 10 ounces.
(c) If one potato is randomly selected, find the probability that
it weighs between 7 and 10 ounces.
In: Statistics and Probability
Suppose my utility function for asset position ? is given by ?(?) = ( ? 1000) 2 . If I have $ 17,000 and I am considering the following two lotteries L1: With probability 1, I lose $1000. L2: With probability .78, I gain $0. With probability .22, I lose $10,000 a) Draw the lotteries and determine which lottery I select based in the utility value b) Determine which lottery I select based in the expected value
In: Statistics and Probability