Calls to a customer service center last on average 2.1 minutes with a standard d

Question

Calls to a customer service center last on average 2.1 minutes with a standard deviation of 1.6 minutes. An operator in the call center is required to answer 63 calls each day. Assume the call times are independent. What is the expected total amount of time in minutes the operator will spend on the calls each day? Give an exact answer. What is the standard deviation of the total amount of time in minutes the operator will spend on the calls each day? Give your answer to four decimal places. What is the approximate probability that the total time spent on the calls will be greater than 148 minutes? Give your answer to four decimal places. Use the standard deviation as you entered it above to answer this question. What is the value c such that the approximate probability that the total time spent on the calls each day is less than c is 0.92? Give your answer to four decimal places. Use the standard deviation as you entered it above to answer this question.

Explanation / Answer

c)

That means that the eman must be greater than 148/63.

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value = 148/63 =    2.349206349      
u = mean =    2.1      
n = sample size =    63      
s = standard deviation =    1.6      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    1.236258797      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.236258797   ) =    0.108181191 [ANSWER]

**********************

d)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.92      
          
Then, using table or technology,          
          
z =    1.40507156      
          
As x = u + z * s / sqrt(n)          
          
where          
          
u = mean =    2.1      
z = the critical z score =    1.40507156      
s = standard deviation =    1.6      
n = sample size =    63      
Then          
          
x = critical value =    2.383235804      

Hence, for 63 calls with this mean,

63x = 2.383235804*63 = 150.1438557 minutes [ANSWER]

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.