when oro it boards used in the manufacture of compact disc players are tested, t
ID: 3306606 • Letter: W
Question
when oro it boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%.LetX : the number of defective boards in a random sample of size n-25, so x ~ Bin(25, 0.05), (Round your probabilities to three deomal paces.) (a) Determine P(X S 2). (b) Determine P(X 2 5). (c) Determine P(1 s X s 4). (d) What is the probability that none of the 25 boards is defective? (e) Calculate the expected value and standard deviation of x. (Round your ståndard deviation to two decimal places.) expected value standard deviation boards boards You may need to use the appropriate table in the Appendix of Tables to answer this question.Explanation / Answer
Solution:-
a) P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2)
= (25C0) * (0.95)^25 * (0.05)^0 + (25C1) * (0.95)^24 * (0.05)^1 + (25C2) * (0.95)^23 *(0.05)^2
= 0.2305 + 0.3650 + 0.2774
= 0.8729
= 0.873(rounded)
b) P(X >= 5) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5))
= 1 - (.2774 + .3650 + .2305 + .0930 + .0269 + .0060)
= 0.0021
= 0.002(rounded)
c) P(1 <= X <= 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
= .3650 + .2305 + .0930 + .0269
= 0.7145
= 0.715(rounded)
d) P(X = 0) = (25C0) * (0.95)^25 * (0.05)^0 = 0.2774
= 0.277(rounded)
e) Expected value = np = 25*0.95 = 23.75
Standard deviation = sqrt npq = sqrt(25*0.95*0.05) = 1.09(rounded)
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