Probability Number Interruptions Working
Please answer the following questions and show working.
1. A new young executive is perplexed at the number of interruptions that occur due to employee relations. She has decided to track the number of interruptions that occur during each hour of her day. Over the last month, she has determined that between 0 and 3 interruptions occur during any given hour of her day. The data is shown below.
Number of Interruptions in 1 hour (X)  Probability (P(X) 


0  .2  
1  .3  
2  .4  
3  .1  
Total 
a) On average, how many interruptions should she expect per hour. (3 points)
b) What is variance and the standard deviation of the interruptions? (2 points)
2. A southwestern tourist city has records indicating that the average daily temperature in summer is 80 degrees F, which is normally distributed with a standard deviation of 3 degrees F.Based on these records, determine:
(a) The probability of a daily temperature between 79 degrees F and 85 degrees F (2 points)
(b) The probability that the daily temperature exceeds 90 degrees F (2 points)
(c) The probability that the daily temperature is below 76 degrees F(2 points)
3) Historical data indicates that only 40% of cable customers are willing to switch companies. If a binomial process is assumed, then in a sample of 15 cable customers, what is the probability that exactly 3 customers would be willing to switch their cable? (3 points)
4. Historical data indicates that only 30% of cable customers are willing to switch companies. If a binomial process is assumed, then in a sample of 20 cable customers, what is the probability that between 2 and 5 (inclusive) customers are willing to switch companies? (3 points)
5. The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 550 and a standard deviation of 40. What is the probability that a student uses fewer than 475 minutes? (2 points)
6. The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50. What is the probability that a student uses more than 375 minutes? (2 points)
7. The time required to travel downtown at 10 a.m. on Monday morning is known to be normally distributed with a mean of 40 minutes and a standard deviation of 5 minutes. What is the probability that it will take less than 35 minutes? (2 points)
8. The time required to travel downtown at 10 a.m. on Monday morning is known to be normally distributed with a mean of 40 minutes and a standard deviation of 5 minutes. What is the probability that it will take between 35 minutes and 44 minutes? (2 points)
Tutor Answer
Hi, please see the following file for the solution..
Please see the following solution.. It involves reading values from the normal distribution table
1. A new young executive is perplexed at the number of interruptions that occur due to employee
relations. She has decided to track the number of interruptions that occur during each hour of her
day. Over the last month, she has determined that between 0 and 3 interruptions occur during any
given hour of her day. The data is shown below.
Number of Interruptions
Probability (P(X)
in 1 hour (X)
0
.2
1
.3
2
.4
3
.1
a) On average, how many interruptions should she expect per hour. (3 points)
b) What is variance and the standard deviation of the interruptions? (2 points)
SOLUTION:
a)
𝑥̅ = (0 × 0.2) + (1 × 0.30) + (2 × 0.40) + (3 × 0.10)
𝑥̅ = 1.4 interruptions
b)
To compute for the variance, we have to setup the following table as follows:
x
P(x)
0
1
2
3
0.2
0.3
0.4
0.1
x*
P(x)
0...
Brown University
1271 Tutors
California Institute of Technology
2131 Tutors
Carnegie Mellon University
982 Tutors
Columbia University
1256 Tutors
Dartmouth University
2113 Tutors
Emory University
2279 Tutors
Harvard University
599 Tutors
Massachusetts Institute of Technology
2319 Tutors
New York University
1645 Tutors
Notre Dam University
1911 Tutors
Oklahoma University
2122 Tutors
Pennsylvania State University
932 Tutors
Princeton University
1211 Tutors
Stanford University
983 Tutors
University of California
1282 Tutors
Oxford University
123 Tutors
Yale University
2325 Tutors