(a) A type of lightbulb is labeled as having an average lifetime of 1000 hours. It's reasonable to model the probability of failure of these bulbs by an exponential density function with mean μ = 1000. (i) Use this model to find the probability that a bulb fails within the first 300 hours. (Round your answer to three decimal places.) 0.259 Correct: Your answer is correct. (ii) Use this model to find the probability that a bulb burns for more than 900 hours. (Round your answer to three decimal places.) 0.407 Correct: Your answer is correct. (b) What is the median lifetime of these lightbulbs? (Round your answer to one decimal place.) 693 Incorrect: Your answer is incorrect. hr

Exercise: counting committees 0.0/2.0 puntos (calificable) we start with a pool of n people. a chaired committee consists of k≥1 members, out of whom one member is designated as the chairperson. the expression k(nk) can be interpreted as the number of possible chaired committees with k members. this is because we have (nk) choices for the k members, and once the members are chosen, there are then k choices for the chairperson. thus, c=∑k=1nk(nk) is the total number of possible chaired committees of any size. find the value of c (as a function of n ) by thinking about a different way of forming a chaired committee: first choose the chairperson, then choose the other members of the committee. the answer is of the form c=(α+nβ)2γn+δ. what are the values of α , β , γ , and δ ?