0. (a) What proportion of lightbulbs last less than 500 hours? (b) What proportion of lightbulbs last longer than 500 hours?

0. (a) What proportion of lightbulbs last less than 500 hours? (b) What proportion of lightbulbs last longer than 500 hours? (c) If we buy two lightbulbs what is the probability that they will both last longer than 500 hours? (d) If we buy two lightbulbs what is the probability that at least one of them lasts longer than 500 hours? 14. Let x be a variable whose distribution is given by f (x) = c(1 - x2 ), -1 < x < 1. (a) What is the value of c? (b) What proportion of the population has an x-value that is between 0 and 0.5? (c) Find the mean of x. (d) Find the standard deviation of x. 15. Let x be a variable whose distribution is given by f (x) = 4x(1 - x2 ), 0 < x < 1. (a) What proportion of the population has an x-value that is greater than 0.5?