Question

16. In order to determine the life expectancy of a particular type of light bulb manufactured by a lighting company, the corporate quality control officer randomly selected 10 bulbs from the pre-packaging section of the company's production line. The bulbs were subsequently tested in the quality control lab and the following data was recorded. Bulb Life (Hours). 3900 s ildedorg eris al terw.o 4200 weelido motus 4100 3800 4000 4300 3600 cools to Tenwo erTAL Tennib jot emotaus a. Calculate the mean life of bulbs in this sample. Mean = Biomolaus OMAAN b. Calculate the standard deviation for the life of bulbs in this sample. Ils one Standard deviation = c. Assuming that the life of this type of bulb produced by this company is normally distributed, find the 98% confidence interval estimate for the mean life of bulbs manufactured by this company. Between and d. What is the probability that a six-pack of bulbs (considered to be a random sample of size 6) manufactured by this company will have a mean life expectancy of at least 5000 hours? Probability =

Answer 1

Mean life of bulbs = 1/n Sigma_i = 1^n x_i: n = 7 = 4014.28 standard deviation = squareroot 1/n Sigma_i = 1^n (xi - x^-)^2 = 180.83 98% confidence interval is (x^- plusminus 3.143 times s/squareroot n) (4014.28 plusminus 3.143 times 180.83/squareroot 7) = (4014.28 plusminus 214.82) (3799.46, 4229.10) Between 3799.96 and 4229.10 P(x^- greaterthanorequalto 5000) = P (z greaterthanorequalto 5000 - 4014.28/180.83/squareroot 6) = P(z greaterthanorequalto 1.35) = 0.0885