Acertain system can experience three different types of defects. let ai (i = 1,2,3) denote the event that the system has a defect of type i. suppose that the following probabilities are true. p(a1) = 0.12 p(a2) = 0.07 p(a3) = 0.06 p(a1 ∪ a2) = 0.13 p(a1 ∪ a3) = 0.15 p(a2 ∪ a3) = 0.11 p(a1 ∩ a2 ∩ a3) = 0.01 (a) what is the probability that the system does not have a type 1 defect? (b) what is the probability that the system has both type 1 and type 2 defects? (c) what is the probability that the system has both type 1 and type 2 defects but not a type 3 defect? (d) what is the probability that the system has at most two of these defects?

If f(x)=2x-6 and g(x)=3x+9, find (f-g)(x)

The table shows population statistics for the ages of best actor and best supporting actor winners at an awards ceremony. the distributions of the ages are approximately bell-shaped. compare the z-scores for the actors in the following situation. best actor best supporting actor muequals42.0 muequals49.0 sigmaequals7.3 sigmaequals15 in a particular year, the best actor was 59 years old and the best supporting actor was 45 years old. determine the z-scores for each. best actor: z equals best supporting actor: z equals (round to two decimal places as needed.) interpret the z-scores. the best actor was (more than 2 standard deviations above more than 1 standard deviation above less than 1 standard deviation above less than 2 standard deviations below) the mean, which (is not, is) unusual. the best supporting actor was (less than 1 standard deviation below more than 1 standard deviation above more than 2 standard deviations below more than 1 standard deviation below) the mean, which (is is not) unusual.

This is so hard and it’s for a test