Question 1

A recent market study has determined that the probability that a young adult will 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 _________.
A) 0.1575
B) 0.1612
C) 0.1775
D) 0.1812
E) 0.1975

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 = 0.1094The 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 = 0.0488Therefore, the approximate probability of at least 2 but no more than 3 young adults being willing to try the new service is:P(2 ≤ X ≤ 3) = P(X = 2) + P(X = 3) = 0.1094 + 0.0488 = 0.1582The closest answer choice to 0.1582 is A) 0.1575.

Question 2

If x is uniformly distributed over some interval.The mean value (μ)of x is 2 and its variance (σ²)is 1/3.The probability that x is between 2 and 2.5,P(2 $\le$ x $\le$ 2.5),is _________. A) 0.45 B) 0.40 C) 0.35 D) 0.33 E) 0.25

Accepted Answer

The answer of If x is uniformly distributed over some...

Question 3

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 _________.
A) 0.223
B) 0.202
C) 0.183
D) 0.162
E) 0.143

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 4

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)?
A) 718
B) 716
C) 714
D) 712
E) 710

Accepted Answer

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

Question 5

Participants in a 2 day biking event,cross the finish line at a rate of 10 bike riders per fifteen minute interval.The probability that less than 10 minutes will elapse between car arrivals is _____________.
A) .0001
B) .9987
C) .0013
D) .6667
E) .1667

Accepted Answer

The average time between two bikers crossing the finish line is 1.5 minutes (15 min / 10 riders). Therefore, the probability that less than 10 minutes will elapse between two bikers finishing is the same as the probability that less than 7 bikers will finish in a row without a gap of more than 1.5 minutes between any two of them. This can be calculated using the Poisson distribution with lambda = 7, where lambda represents the number of bikers in the interval. 
P(X<7)=Poisson CDF(7;7)= 0.9987 
Thus, the probability that less than 10 minutes will elapse between car arrivals is .9987.

Question 6

A recent market study has determined that the probability that a young adult will 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)_________.
A) 0.251; 0.246
B) 0.246; 0.251
C) 0.246; 0.248
D) 0.249; 0.251
E) 0.251; 0.249

Accepted Answer

The answer of A recent market study has determined that...

Question 7

Inquiries arrive at a record message device according to a Poisson process of rate 15 inquiries per minute.The probability that it takes more than 12 seconds for the first inquiry to arrive is approximately _________
A) 0.05
B) 0.75
C) 0.25
D) 0.27
E) 0.73

Accepted Answer

The probability that it takes more than 12 seconds for the first inquiry to arrive is given by the exponential distribution with parameter 15 inquiries per minute. The probability that it takes more than 12 seconds is given by:P(X > 12) = e^(-15 * 12/60) = 0.27

Question 8

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.
A) 0.03
B) 0.05
C) 0.5
D) 1
E) 2

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.

Question 9

Participants in a 2 day biking event,cross the finish line at a rate of 10 bike riders per fifteen minute interval.The probability that at least 2 minutes will elapse between bike riders is _____________.
A) .0000
B) .0498
C) .2635
D) .1353
E) .4647

Accepted Answer

We can use Poisson distribution to model the arrival of bikers at the finish line. Let λ be the expected number of bikers finishing per 15 minute interval. Then λ = 10.

To find the probability that at least 2 minutes will elapse between bike riders, we can find the probability that no bike riders finish in a 2 minute interval. Let X be the number of bikers that finish in a 2 minute interval. Then X has a Poisson distribution with mean μ = 10*(2/15) = 4/3.

P(X = 0) = e^(-μ)μ^0/0! = e^(-4/3) ≈ 0.2635

Therefore, the answer is (C).

Question 10

If variable x is normally distributed with mean 0 and standard deviation 1,x ~ N(0,1),then the probability that x is exactly 0 is _________.
A) 0.05
B) 0.04
C) 0.02
D) 0.01
E) 0.00

Accepted Answer

The probability of a continuous random variable taking on a specific value (in this case, x = 0) is always equal to zero. Therefore, the answer is 0.

Quiz 6: Continuous Distributions

If x is uniformly distributed over some interval.The mean value (μ) of x is 2 and its variance (σ²) is 1/3.The probability that x is between 2 and 2.5,P(2 $\le$ x $\le$ 2.5) ,is _________.

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 _________.

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) ?

Participants in a 2 day biking event,cross the finish line at a rate of 10 bike riders per fifteen minute interval.The probability that less than 10 minutes will elapse between car arrivals is _____________.

Inquiries arrive at a record message device according to a Poisson process of rate 15 inquiries per minute.The probability that it takes more than 12 seconds for the first inquiry to arrive is approximately _________

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.

Participants in a 2 day biking event,cross the finish line at a rate of 10 bike riders per fifteen minute interval.The probability that at least 2 minutes will elapse between bike riders is _____________.

If variable x is normally distributed with mean 0 and standard deviation 1,x ~ N(0,1) ,then the probability that x is exactly 0 is _________.