We are currently working with a researcher who focuses on auditory services. This researcher has data measuring dominant ear scores measuring perceived sounds. This data follows a normal distribution with a mean of 75 and variance of 9. Use this information to answer the following questions. a) What is the probability a person has a depression score of 81? b) What is the probability a person has an ear score of greater than 69? c) What is the probability a person has an ear score of at most 77? d) What is the probability a person has an ear score between 71 and 79? e) What is the probability a person has a depression score of 73? 2. Let Z follow a standard Normal distribution a) Find P(Z > -1.27) b) Find P(Z < 0) c) Find P(Z > 2.69) d) Find P(Z < 6.37) e) Find P(-1.78 < Z < -0.56) f) Find the constant c such that P(Z < c) = 0.95 g) Find the constant c such that P(-c< Z < c) = 0.90 3. Cochlear implants are set to last a lifetime, however, manufacture only insure it for up to 10 years. In other words, the failure time for a cochlear implant follows an exponential distribution with a mean of 10 years. a) What's the probability that the implant will last up to 15 years? b) What's the probability that the implant will last between 5 and 15 years? c) What's the probability that the implant will last beyond 20 years? 4. Find the following statistic or probability: a) P(t(25) -2.01) b) t(55),0.55 c) P(0.528 t(95) 1.301) d) t(25),0.70 e) P(t(62) c) = 0.37

f) (2 15 > 11.59) g) ( 2 75 < 45.6) h) 2 27, 0.90 i) ((55,35) < 3.07)

j) ((50,75) > )=0.32