Download Final Exam - Statistics for Engineering | STAT 4705 and more Exams Statistics in PDF only on Docsity! STAT 4705
1.
Final Exam = May 7,2001 Name.
Components used in an assembly arrive in boxes of 24. Before the components are installed in an
assembly, a sample of 3 components from each box is selected and inspected. Each component in the
sampie is classified as grade A, grade B, or grade C, where grades B and C indicate lower than
standard quality. Suppose that a box arrives with 18 grade A components, 4 grade B components, and
2 grade C components.
(a) Find the probability that the sample of 3 from this box will contain one grade B component and
one grade C component.
(b) If the sample contains exactly one grade C component, find the conditional probability that it also
contains exactly one grade B component.
Suppose that a random variable X has an exponential distribution with density
f)=(/ Ble 8, x>0.
(a) Show that the cumulative distribution function of X is
F(xj=l-e*/F, x20.
(b) A sample of 36 observations was collected using a standard UNIX program called “ping” to
measure the time (ms) taken to reach, and receive a reply from, another computer on ‘the Internet, ~
The sample mean is ¥ = 438.3 and the sample standard deviation is S = 261.5.
310 1450 222680 299 157-202 525 568
447 129 253 406 33] 644 822 461 292
204 396 684 517 322 536 343 259 526
288 330 262 205 294 496 1043 366 S11
interval observed frequency
0-300 13
300-600 i7
600-900 4
above 900 2
It has been claimed that the distribution of the time to receive a reply is exponential with a mean
of 8 = 400. However, a histogram based on the intervals and observed frequencies above
suggests that the assumption of an exponential distribution may be questionable. Test the
hypothesis that the distribution is exponential with # = 400. Use a = .05 and state your
conclusion.
An experiment was done to study the accuracy of a wave-function generator. The experiment was
carried out by comparing the setting of the dial frequency to measurements of the generated frequency.
The goal of the experiment was to see how well the dial settings corresponded to the measured
frequencies. The data shown in the table below are the dial settings x (Hz.) and the measured
frequencies y (Hz.) for ten cases.
Dial 100 200 300 400 500 600 700 800 900 1000
Measure | 112 210 318 421 516 630 738 827 945 1060
d
For these data Yx,=5500, Six? =3,850,000, Yiy; =3777, Uy? = 4,243,363, Yx,y, = 4,041,700,
Sy = 825000, Sy, =905990.1, and Sp, = 864350.
