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Suppose Ralphie V's exam percentage on any exam at CU can be described by a random variable X where X~ N(75,52). for the following questions, where appropriate,express your answer in terms of ?, the cdf of the standard normal distribution

a) Ralphie's parents will pay ralphie $20 if she gets more than 95% on any exam. what is the probability that ralphie will make $20 on any given exam?

b) Assuming ralphie's performance on each exam is independent,and supposing ralphie takes 10 exams a year, find the probability that ralphie will make at least $20 over the course of the 10 exams.

c) Ralphie never skips an exam,even if she is sick. The probability that Ralphie will be sick on any given exam day is ps, for some ps belongs to(0,1). The distribution of X, given that ralphie is sick, is X~ N(75,52).

repeat parts (a) and (b)

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