Homework 3 Chapter 5 & 6

QUESTION 1
1. ch 5 The number of  finance majors within the School of Business is an example of
 
 a continuous random variable
 
 a constant
 
 the Poisson distribution
 
 the normal distribution
 
 a discrete random variable
2 points  
QUESTION 2
1. ch 5
A recent analysis of the number of rainy days per month found the following outcomes and probabilities.
Number of Raining Days (x) P(x)
3 .40
4 .20
5 .40
The mean of this distribution is

 
 2
 
 4
 
 5
 
 <1
 
 3
2 points  
QUESTION 3
1. ch 5 (hint: you can use table on p 785 or Excel).  A student randomly guesses the answers to a five question true/false test. If there is a 50% chance of guessing correctly on each question, what is the probability that the student misses exactly 1 question?
 
 0.031
 
 0.156
 
 0.200
 
 0.073
 
 0.001
2 points  
QUESTION 4
1. ch 5 (hint you can use table on p 785 or Excel)  A student randomly guesses the answers to a five question true/false test.  If there is a 50% chance of guessing correctly on each question, what is the probability that the student misses no questions?
 
 1.000
 
 0.200
 
 0.000
 
 0.031
 
 0.500
2 points  
QUESTION 5
1. ch 5 (Hint: you can use table on p 786 or Excel)  Melissa, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system, and orders an inspection of a random sample of vouchers issued since January 1, 2006.  A sample of ten vouchers is randomly selected, without replacement, from the population of 2,000 vouchers. Each voucher in the sample is examined for errors and the number of vouchers in the sample with errors is denoted by x. If 20% of the population of vouchers contain errors, P(x>0) is
 
 1.0000
 
 0.3020
 
 0.1074
 
 0.8171
 
 0.8926
2 points  
QUESTION 6
1. ch 5 (hint: you can use table on p 785 or Excel)  Craig purchased a mailing list of 2,000 names and addresses for her mail order business, but after scanning the list he doubts the authenticity of the list.  He randomly selects five names from the list for validation.  If 40% of the names on the list are non-authentic, and x is the number of non-authentic names in her sample, P(x=0) is
 
 0.0778
 
 0.0467
 
 0.8154
 
 0.5000
 
 0.4000
2 points  
QUESTION 7
1. ch 5 (Hint: can use Excel or table on page 792)  Richard counts the number of cars arriving at a toll booth in five-minute intervals, which is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals. The probability of 3 cars arriving over a five-minute interval is _______. Hint: the mean is lambda
 
 0.0498
 
 0.0020
 
 0.2700
 
 0.2240
 
 0.0001
2 points  
QUESTION 8
1. ch 6.1  If the number of parking spots at grocery stores is uniformly (hint) distributed over the interval 90 to 140, inclusively (90 ≤ x ≤ 140), inclusively (90 ≤ x ≤ 140), then the mean of this distribution is
 
 70
 
 230
 
 115
 
 45
 
 unknown
2 points  
QUESTION 9
1. ch 6.1  If the number of parking spots at urban grocery stores is uniformly (hint) distributed over the interval 90 to 140, inclusively (90 ≤ x ≤ 140), then the standard deviation of this distribution is
 
 4.16
 
 14.4
 
 50
 
 7.07
 
 28.2
2 points  
QUESTION 10
1. ch 6.2 (hint: you can use the front cover table)  Let z be a normal random variable with mean 0 and standard deviation 1. What is P(z > 2.4)?
 
 0.4793
 
 0.4918
 
 0.0082
 
 0.9918
 
 0.0820
2 points  
QUESTION 11
1. ch 6.4  The exponential distribution is an example of
 
 a discrete distribution
 
 a continuous distribution
 
 a normal distribution
 
 a symmetrical distribution
 
 a bimodal distribution
2 points  
QUESTION 12
1. ch 6.4 During the summer at a small private airport, the unscheduled arrival of airplanes is Poisson distributed with an average arrival rate of 1.12 plane per hour. What is the average interarrival time between planes? (Hint: lambda is the average arrival rate)
 
 .89 hr, or 53.4 minutes
 
 .56 hr, or 32 minutes
 
 .83 hr, or 50 minutes
 
 .25 hr or 15 minutes
2 points  
QUESTION 13
1. ch 6 find the probability for the following expoential distribution:  P(x > 3½  λ = 1.3):
Hint: this is similar to problem 6.29 on page 213

 
 .0390
 
 .0211
 
 .0202
 
 .0324
2 points  
QUESTION 14
1. ch 6 Melissa and Priscilla opened a small dress store in a mall. During the first few weeks, business was slow, with the store averaging only 3 customers per hour in the morning (lambda). Assume that the random arrival of customers is Poisson distributed. What is the probability that at least one hour would elapse between customers? Hint: this is similar to p213 problem 6.29.
 
 .0634
 
 .0399
 
 .0512
 
 .0498