A computer lab at a small college has 25 computers. Twice during the day, a full

Question

A computer lab at a small college has 25 computers. Twice during the day, a full scan for viruses is performed on each computer. Because of differences in the configuration of the computers, the times required to complete the scan are different for each machine. Records for the scans are kept and indicate that the time (in seconds each machine is as shown here. Complete parts a through c below. required to perform the scan for 1,528 1,649 1,686 1,309 1,224 1,283 1.407 1,308 1,810 1,825 1,570 1,259 1,739 1,513 1,581 1,278 1,122 1,546 1,030 1,648 1,143 1,287 1,322 1,816 1,722 a. What is the mean time required to scan all 25 computers? The mean time required to scan all 25 computers is (Type an integer or a decimal. Do not round.) b. Suppose a random sample of 5 computers is taken and the scan times for each are as follows: 1,816, 1,648, 1,546, 1.287, and 1,259 .If these 5 randomly sampled computers are used to estimate the mean scan time for all 25 computers, what would the sampling error be? The sampling error for the sample mean is (Type an integer or a decimal. Do not round.) c. What is the range of possible sampling errors if a random sample size of 7 computers is taken to estimate the mean scan time for all 25 machines? The possible sampling errors range fromto (Round to two decimal places as needed. Use ascending order.)

Explanation / Answer

Solution:- given that values :1528,1649,1686,1309,1224,1283,1407,1308,1810,1825,1570,1259,1739,1513,1581,1278,1122,1546,1030,1648,1143,1287,1322,1816,1722

a) the mea time required to scan all computers is 1464.2

Explanation:-

mean = sum of terms/no of terms

=   36605/25

= 1464.2

b) the sampling error for the sample mean is 47

sampling error = X - mu = 1511.2 -  1464.2 = 47

c) The possible sampling errors range from -272.9143 to 285.3714

Explanation:-

range of the for the sampling error of n= 7, the sampling error is 7 smallest sample values of size n = 7 are

1030 1122 1143 1224 1259 1278 1283

X = 1191.2857
There fore population mean = 1464.2
sampling error = 1191.2857 - 1464.2 = -272.9143

The largest sample values o size n = 7 are 1649 1686 1722 1739 1810 1816 1825
  
X = 1749.5714
There fore population mean = 1464.2
sampling error = 1749.5714 - 1464.2 = 285.3714  

  

  

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