You are asked to match three songs with the performers who made those songs famous. If you guess, the probability distribution for the number of correct matches is:

Probability0.3330.5000.0000.167Number correct0123

What is the probability you will get:

a.Exactly one correct?(Round the final answer to 3 decimal places.)

b.At least one correct?(Round the final answer to 3 decimal places.)

c.Exactly two correct?(Round the final answer to 3 decimal places.)

d.Compute the mean, variance, and standard deviation of this distribution.(Round the final answers to 3 decimal places.)

Mean

Variance ²

Standard deviation