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A sample of 200 bulbs made by a company give a lifetime mean of 1540 hours with a standard deviation of 42 hours. Is it likely that the sample has been drawn from a population with a mean lifetime of 1500 hours? You may use 5 percent level of significance |
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Answer» Probability of manufacturing a defective bulb = 2% = 0.02Probability of manufacturing a good bulb = 1 - 0.02 = 0.98Using the formula for binomial distribution :\sum_{N=0}^{r}_{r}^{n}\textrm{C}\cdot p^r\cdot q^{n-r}LET X be the random variable for manufacturing the defective bulbsa). n = 200 bulbs and r = 2P(X < r = 2) = \sum_{n=0}^{2}_{r}^{200}\textrm{C}\cdot 0.02^r\cdot 0.98^{200-r}\\\\P(X < r = 2) = _{0}^{200}\textrm{C}\cdot 0.02^0\cdot 0.98^{200-0}+_{1}^{200}\textrm{C}\cdot 0.02^1\cdot 0.98^{199}\\\\\implies P(X < r = 2) =0.0894b). n = 200 and r = 3P(X < 4 ) = P(X < 2) + P(2) + P(3) = 0.0894 + 0.34212 = 0.43⇒ P(X > 3) = 1 - 0.43 = 0.57 |
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