Question

Eyeglassomatic manufactures eyeglasses for different retailers. The number of days it takes to fix defects in an eyeglass and the probability that it will take that number of days are in the table. Table #5.1.8: Number of Days to Fix DefectsNumber of daysProbabilities

1 24.9%

2 10.8%

3 9.1%

4 12.3%

5 13.3%

6 11.4%

7 7.0%

8 4.6%

9 1.9%

10 1.3%

11 1.0%

12 0.8%

13 0.6%

14 0.4%

15 0.2%

16 0.2%

17 0.1%

18 0.1%

State the random variable.

b.)Draw a histogram of the number of days to fix defects

c.)Find the mean number of days to fix defects.

d.)Find the variance for the number of days to fix defects

. e.)Find the standard deviation for the number of days to fix defects.

f.)Find probability that a lens will take at least 16 days to make a fix the defect.

g.)Is it unusual for a lens to take 16 days to fix a defect?

h.)If it does take 16 days for eyeglasses to be repaired, what would you think?

Answer 1

b)

c)

x	P(x)	xP(x)	x2P(x)
1	0.249	0.249	0.249
2	0.108	0.216	0.432
3	0.091	0.273	0.819
4	0.123	0.492	1.968
5	0.133	0.665	3.325
6	0.114	0.684	4.104
7	0.07	0.490	3.430
8	0.046	0.368	2.944
9	0.019	0.171	1.539
10	0.013	0.130	1.300
11	0.01	0.110	1.210
12	0.008	0.096	1.152
13	0.006	0.078	1.014
14	0.004	0.056	0.784
15	0.002	0.030	0.450
16	0.002	0.032	0.512
17	0.001	0.017	0.289
18	0.001	0.018	0.324
	total	4.175	25.845
	E(x) =μ=	ΣxP(x) =	4.1750
	E(x2) =	Σx2P(x) =	25.8450
	Var(x)=σ2 =	E(x2)-(E(x))2=	8.4144
	std deviation=	σ= √σ2 =	2.901

mean number of days to fix defects =4.175

d)

variance =8.4144

e)

std deviation =2.901

f)

probability that a lens will take at least 16 days to make a fix the defec =P(X=16)+P(X=17)+P(X=18)

=0.002+0.001+0.001 =0.004

g)

Yes as this has probability of having less then 0.05

h)

we have reason to thick either the problem is complex or the problem is not being attended properly