Times between successive crashes of a computer system were generated for a 6-months period and are given in increasing order as follows (time in hours): 1, 10, 20, 30, 40, 52, 63, 70, 80, 90, 100, 102, 130, 140, 190, 210, 266, 310, 530,590, 640, 1340. The value of parameter α and Mean (1/α) is given as 0.00435 and 230 hrs, respectively. Use kolmogrov-Smirnov test to examine the goodness of fit of exponential distribution.
A newspaper publisher, trying to pinpoint his market’s characteristics wondered whether newspaper readership in the community is related to readers’ educational achievement. A survey questioned adults in the area on their level of education and their frequency of readership. The results are shown in the following table:
| Frequency of Readership | Level of Educational Achievement | |||
| Professional or postgraduates | College graduates | High school grad | Did not complete high school | |
| Never | 10 | 17 | 11 | 21 |
| Sometimes | 12 | 23 | 8 | 5 |
| Morning or evening | 35 | 38 | 16 | 7 |
| Both editions | 28 | 19 | 6 | 13 |
In a certain book, there is one misprint per two pages, on the average. What is the probability that there are two or more misprints on a randomly chosen page?
Twelve samples of 4 LED bulbs were selected at regular intervals from a LED bulbs manufacturing company. If bulbs have mean life equal to 2000 hours, it is considered satisfactory. The SD of life of the bulbs is expected to be 520 hours. On testing the samples, the failure times (in hours) were recorded and given below:
| Sample 1 | Sample 2 | Sample 3 | Sample 4 | Sample 5 | Sample 6 | Sample 7 | Sample 8 | Sample 9 | Sample 10 | Sample 11 | Sample 12 |
| 2081 | 1528 | 1984 | 1728 | 1804 | 2002 | 1994 | 1616 | 1982 | 2132 | 2134 | 1749 |
| 1363 | 1330 | 2384 | 1972 | 1845 | 1804 | 2023 | 1832 | 2342 | 1998 | 2140 | 1948 |
| 2092 | 2053 | 2194 | 1647 | 2132 | 1760 | 2136 | 1497 | 2132 | 1554 | 1756 | 2050 |
| 2385 | 1945 | 1456 | 1792 | 2024 | 2035 | 1842 | 1692 | 1994 | 1777 | 1994 | 1857 |
From the following data find mean and variance of the stratified sampling under (i) proportional and (ii) Neyman Allocation
| Strata | Ni | Ni | Si | |
| 1 | 80 | 29 | 12 | 80 |
| 2 | 160 | 39 | 8 | 30 |
| 3 | 260 | 32 | 4 | 10 |
| 500 | 100 |
Arrivals at telephone booth are considered to be Poisson with an average time of 10 minutes between are arrival and the next. The length of phone call is assumed to be distributed exponentially with mean 3 minutes
Two cards are drawn one at a time from a 52-card standard deck. Then the probability that the second card is red, if the drawing is done with replacement is 1/2
Solve the following LPP using graphical method:
Maximize Z = 3x1 + 2x2
Subject to the Constraints:
-2x1 + x2 ≤ 1
x1 ≤ 2
x1 + x2 ≤ 3
x1, x2 ≥0