The life of a watch battery is normally distributed with a mean of 950 days and standard deviation of 40 days. Using the appropriate Excel functions (see Chapter 5), determine the following:

a. What fraction of batteries is expected to survive beyond 1,010 days?

b. What fraction will survive fewer than 900 days?

c. Draw a graph of the reliability function using Excel.

d. What length of warranty is needed so that no more than 10 percent of the batteries can be expected to fail during the warranty period?

 

Watch Battery Life-Reliability
Enter data only in the shaded cells
This spreadsheet is designed to calculate the probability of values equal to, or less than, a desired x value,
given the mean and standard deviation of a normally distributed variable. It uses the cumulative normal distribution
Enter the mean of the distribution in shaded cell D8 and the standard deviation in shaded cell D9. below.
Enter the desired X-value in shaded cell D10, below. The calculated z-value and probability will be seen in D11 and D12.
Mean of distribution		950		950
Std deviation of distribution		40		40
Desired x-value		1010		900
Calculated z-value		1.50		-1.25
Probability of x, or less		0.93319		0.10565
	(X-axis)	Probability Using
Desired x-values	Equivalent - Z Values	NORMS.DIST
790	-4.00	0.00003
794	-3.90	0.00005
798	-3.80	0.00007
802	-3.70	0.00011
806	-3.60	0.00016
810	-3.50	0.00023
814	-3.40	0.00034
818	-3.30	0.00048
822	-3.20	0.00069
826	-3.10	0.00097
830	-3.00	0.00135
834	-2.90	0.00187
838	-2.80	0.00256
842	-2.70	0.00347
846	-2.60	0.00466
850	-2.50	0.00621
854	-2.40	0.00820
858	-2.30	0.01072
862	-2.20	0.01390
866	-2.10	0.01786
870	-2.00	0.02275
874	-1.90	0.02872
878	-1.80	0.03593
882	-1.70	0.04457
886	-1.60	0.05480
890	-1.50	0.06681
894	-1.40	0.08076
898	-1.30	0.09680
902	-1.20	0.11507
906	-1.10	0.13567
910	-1.00	0.15866
914	-0.90	0.18406
918	-0.80	0.21186
922	-0.70	0.24196
926	-0.60	0.27425
930	-0.50	0.30854
934	-0.40	0.34458
938	-0.30	0.38209
942	-0.20	0.42074
946	-0.10	0.46017
950	0.00	0.50000
954	0.10	0.53983
958	0.20	0.57926
962	0.30	0.61791
966	0.40	0.65542
970	0.50	0.69146
974	0.60	0.72575
978	0.70	0.75804
982	0.80	0.78814
986	0.90	0.81594
990	1.00	0.84134
994	1.10	0.86433
998	1.20	0.88493
1002	1.30	0.90320
1006	1.40	0.91924
1010	1.50	0.93319
1014	1.60	0.94520
1018	1.70	0.95543
1022	1.80	0.96407
1026	1.90	0.97128
1030	2.00	0.97725
1034	2.10	0.98214
1038	2.20	0.98610
1042	2.30	0.98928
1046	2.40	0.99180
1050	2.50	0.99379					Fantastic news! We've Found the answer you've been seeking! Answer rating: 66% (3 reviews) a b c The reliability function looks approximately as follows d Using t...View the full answer Answered By Kennedy Odhiambo As a professional writer, I have been in the field for over 5 years having worked as a lecture in different tertiary institutions across the world. With this impeccable experience, I assure provision of a good and supporting environment for students to learn. 5.00+ 2+ Reviews 10+ Question Solved Related Book For   An Introduction To Six Sigma And Process Improvement ISBN: 9781133604587 2nd Edition Authors: James R. Evans, William M. Lindsay See More Books Question Posted: Jul 26, 2023 09:35 AM See More Questions Students also viewed these Business questions The life of an automotive battery is normally distributed with mean 900 days and standard deviation 35 days. What fraction of these batteries would be expected to survive beyond 1,000 days? 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