Question 1

A recent market study has determined that the probability that a young adult would be willing to try a new online financial service that your company is offering is 50%.In a random sample of 10 young adults, the approximate probability that at least 2 but no more than 3 will be willing to try this new service is _________.

Accepted Answer

The probability of at least 2 but no more than 3 young adults being willing to try the new service can be calculated using the binomial distribution. The probability of exactly 2 young adults being willing to try the service is given by:P(X = 2) = (10 choose 2) * (0.5)^2 * (0.5)^8 = 0.1575The probability of exactly 3 young adults being willing to try the service is given by:P(X = 3) = (10 choose 3) * (0.5)^3 * (0.5)^7 = 0.1612Therefore, the approximate probability that at least 2 but no more than 3 young adults will be willing to try the new service is:P(X >= 2 and X <= 3) = P(X = 2) + P(X = 3) = 0.1575 + 0.1612 = 0.3187

Question 2

Most graduate business schools require applicants to take the GMAT.Scores on this test are approximately normally distributed with a mean of 545 points and a standard deviation of 100 points.What score do you need to be in the top 5% (approximately the scores needed for top schools)?

Accepted Answer

The answer of Most graduate business schools require applicants to...

Question 3

A recent market study has determined that the probability that a young adult would be willing to try a new online financial service that your company is offering is 50%.In a random sample of 10 young adults, the probability that exactly 5 will be willing to try this new service is _________, and the approximate probability (using the normal distribution is)_________.

Accepted Answer

The probability of exactly 5 out of 10 trying the service is calculated using the binomial distribution formula, which gives 0.246. The normal approximation to the binomial distribution also gives approximately 0.248.

Question 4

Employees arrive at a cafeteria according to a Poisson process at an average rate of 30 employees per hour.The probability that after one employee arrives, the next one will arrive at least 3 minutes later is _________.

Accepted Answer

The Poisson process implies that the time between arrivals follows an exponential distribution with parameter λ, where λ is the average rate of arrivals per unit time. Given λ = 30 employees per hour, or 0.5 employees per minute (since 30 employees/hour * 1 hour/60 minutes = 0.5 employees/minute), the probability that the time until the next arrival is at least t minutes is given by P(T ≥ t) = e^(-λt). For t = 3 minutes, P(T ≥ 3) = e^(-0.5*3) = e^(-1.5) ≈ 0.223.

Question 5

Employees arrive at a cafeteria according to a Poisson process at an average rate of 30 employees per hour.The average waiting time between employees' arrivals is _________ minutes.

Accepted Answer

2The average waiting time between arrivals in a Poisson process is the inverse of the average rate of arrival. Since the rate is 30 employees per hour, the average waiting time is 1/30 hours. Converting hours to minutes (1 hour = 60 minutes), we get (1/30) * 60 = 2 minutes.

Quiz 6: Continuous Distributions

Most graduate business schools require applicants to take the GMAT.Scores on this test are approximately normally distributed with a mean of 545 points and a standard deviation of 100 points.What score do you need to be in the top 5% (approximately the scores needed for top schools) ?

Employees arrive at a cafeteria according to a Poisson process at an average rate of 30 employees per hour.The probability that after one employee arrives, the next one will arrive at least 3 minutes later is _________.

Employees arrive at a cafeteria according to a Poisson process at an average rate of 30 employees per hour.The average waiting time between employees' arrivals is _________ minutes.