Probability: Deceit Someone please help me. My online statistics class isn't able to give me the help i need to confidently perform this problem.

85% of those trained were able to pass the polygraph examination even when guilty of a crime. suppose that a random sample of 9 students are told a "secret" and then given instructions on how to pass the polygraph examination without revealing the secret. what is the probability that: a) all the students are able to pass the polygraph examination? b) more than half the students are able to pass the polygraph examination? c) no more than four of the students are able to pass the polygraph examination? d) all the students fail the polygraph examination?

I put it into the calculator with binompdf. My n=9, probability of success=.85. For part (a) i got .23162. Am I doing this right?

Find the center and the radius of the circle with the equation: x^2-2x+y^2+4y+1=0?

Which of the following are independent events? a) knowing that it is going to rain tomorrow, and bringing an umbrella to schoolb) knowing that you have to get up early tomorrow, and going to bed before 9 p.mc) knowing that it is going to rain tomorrow, and going to bed before 9 p.md) knowing that you have a test in school tomorrow, and studying thw night before

Ascientist studied a population of workers to determine whether verbal praise and/or tangible rewards affect employee productivity. in the study, some workers were offered verbal praise, some were offered tangible rewards (gift cards, presents, and some were offered neither. the productivity of each participant was measured throughout the study by recording the number of daily tasks completed by each employee. which inference might the scientists make based on the given information? a.) the number of daily tasks completed by each employee may influence the dependent variable, which is whether the employee receives verbal praise, tangible rewards, or neither. b.) verbal praise and/or tangible rewards may influence the independent variable, which is the number of daily tasks completed by each employee. c.) verbal praise and/or tangible rewards may influence the dependent variable, which is the number of daily tasks completed by each employee. d.) the dependent variables, which are verbal praise and tangible rewards, may influence the number of daily tasks completed by each employee.