Question

Question 6 of 8 (1 point) Attempt 1 of Unlimited 3.2 Section Exercise Time to review: The following table presents the time taken to review articles that were submitted for publication to a particular journal during a recent year. A few articles took longer than 6 months to review; these are omitted from the table. Consider the data to be a population. Number of Articles TA Time (Months) 0-0.9 44 16 1.0-1.9 2.0 - 2.9 3.0-3.9 17 20 4.0-4.9 12 allo 5.0-5.9 15 Send data to Excel (a) Approximate the variance of the times. Round the answer to at least two decimal places. The variance is (b) Approximate the standard deviation of the times. Round the answer to at least two decimal places. The standard deviation is

Answer 1

class	f	X	fX	X bar	(Xi-Xbar)^2	f*(Xi-Xbar)^2
0-0.9	44	0.45	19.8	2.32903	3.5307622	155.353538
1-1.9	16	1.45	23.2	2.32903	0.7726977	12.36316337
2-2.9	17	2.45	41.65	2.32903	0.0146332	0.248764308
3-3.9	20	3.45	69	2.32903	1.2565687	25.13137357
4-4.9	12	4.45	53.4	2.32903	4.4985042	53.98204995
5-5.9	15	5.45	81.75	2.32903	9.7404396	146.1065947
total	124	17.7	288.8		19.813606	393.1854839

Solution ; a variance = noitrinh rob Ef (x-7)? Zf Fi 393.1855 124 variance 3.17

b) standard deviation S.D. = EF(X-)? Ef 3991855 124 v3.17 6 = 1.78 Given. The mean temperature standard deviation 76.5°F 5.3°F K chebysher's inequality - Plla-Kbx ste Mx tkox), 1-162 22 :P 76.5-2(5:3) < X < 76.57.21513)} > 1-3 ples.g4X4 871) 7 3 - P(65.9 < X < 871) 7 0.75.

Date The proportion of values from a data set that will fall within within k=2 standard deviations of mean will be at least ft- K² K J1004 1 - = 3/4 319 = 0.75 (?- Kios 5o. 3 757 At least 757. temperature 87.1°F of the days had between 65.9 °F and