Math Stats Problem?

When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let X = the number of defective boards in a random sample of size n = 25, so X ~ Bin(25, .05).





a. Determine P(X %26lt;= 2)


b. Determine P(X %26gt;= 5)


c. Determine P(1 %26lt;= X %26lt;= 4)


d. What is the probability that none of the 25 boards is defective?

Math Stats Problem?
P(X = 0) = (25C0) * (0.95)^25 * (0.05)^0 = 0.2774


P(X = 1) = (25C1) * (0.95)^24 * (0.05)^1 = 0.3650


P(X = 2) = (25C2) * (0.95)^23 * (0.05)^2 = 0.2305


P(X = 3) = (25C3) * (0.95)^22 * (0.05)^3 = 0.0930


P(X = 4) = (25C4) * (0.95)^21 * (0.05)^4 = 0.0269


P(X = 5) = (25C5) * (0.95)^20 * (0.05)^5 = 0.0060





a) P(X %26lt;= 2) =


P(X = 2) + P(X = 1) + P(X = 0) =


0.2774 + 0.3650 + 0.2305 =


0.8729 =


87.29%





b) P(X %26gt;= 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=


0.21%





c) P(1 %26lt;= X %26lt;= 4) =


P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) =


.3650 + .2305 + .0930 + .0269 =


0.7145 =


71.45%





d) P(X = 0) =


.2774 =


27.74%