Assume that the following events are independent:

• probability that a randomly selected person has red hair is 0.14
• probability that a randomly selected person has red hair and a female is 0.06

what is the probability that a randomly selected person is a female, given that the person selected has red hair? (round to hundredths)

Suppose a triangle has two sides of length 32 and 35, and that the angle between these two sides is 120°. which equation should you solve to find the length of the third side of the triangle?

The probability that you roll a two on a six-sided die is 1 6 16 . if you roll the die 60 times, how many twos can you expect to roll

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.