There are 76 men and 69 women in a room. 29 of the men and 23 of the women earn more than $50,000 per year.

1. what is the probability of randomly selecting a person that earns more than $50,000 per year from this group?

The american academy of pediatrics wants to conduct a survey of recently graduated family practitioners to assess why they did not choose pediatrics for their specialization. provide a definition of the population, suggest a sampling frame, and indicate the appropriate sampling unit.

Prove that the value of the expression 7^8–7^7+7^6 is divisible by 43.

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.