Question: Hello, could you please help me out I am stuck. Thank you 2.A new vaccine has an 70% success rate for males and 40% success

Hello, could you please help me out I am stuck. Thank you

2.A new vaccine has an 70% success rate for males and 40% success rate for females. Assume that there are about 50% females and males in the population.

(a) A randomly selected person from our class is given the vaccine, and the vaccine turned out to be effective. What is the probability that the person was male?

(b)What is the probability that the person was female?

(c)What is the probability of the vaccine being effective in general (i.e. not conditioned on gender)?

(d) Now assume that everyone in our class was given the vaccine and of the 25 of the students, the vaccine was effective for 17 of you. Using this data as a random sample, construct a 95% confidence interval for the population success rate for this vaccine. Interpret the interval in context of the problem.

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