=35 Let X and Y be normally distributed with X-N(14, a) and Y~N(22, a), a >...

Transcribed Image Text:

=35 Let X and Y be normally distributed with X-N(14, a) and Y~N(22, a), a > 0. a. Find b so that P(X > b) = P(Y < b). b. Is is given that P(X > 20) = 0.112. Find P(16 < Y < 28). 6. The time it takes Suzi to drive from home to work each day is normally distributed with a mean of 35 minutes and a standard deviation of minutes. On 25% of the days, it takes Suzi longer than 40 minutes to drive to work. a. Find the value of b. On a randomly selected day, find the probability that Suzi's drive to work will take longer than 45 minutes. Suzi will be late to work if it takes her longer than 45 minutes to drive to work. The time it takes to drive to work each day is independent of any other day. Suzi will work 5 days next week. c. Find the probability that Suzi will be late to work at least one day next week. d. Given that Suzi will be late to work at least one day next week, find the probability that she will be late less than three times. Suzi will work 22 days this month. She will receive a bonus if she is on time at least 20 of those days. So far this month, she has worked 16 days and been on time 15 of those days. e. Find the probability that Suzi will receive a bonus. =35 Let X and Y be normally distributed with X-N(14, a) and Y~N(22, a), a > 0. a. Find b so that P(X > b) = P(Y < b). b. Is is given that P(X > 20) = 0.112. Find P(16 < Y < 28). 6. The time it takes Suzi to drive from home to work each day is normally distributed with a mean of 35 minutes and a standard deviation of minutes. On 25% of the days, it takes Suzi longer than 40 minutes to drive to work. a. Find the value of b. On a randomly selected day, find the probability that Suzi's drive to work will take longer than 45 minutes. Suzi will be late to work if it takes her longer than 45 minutes to drive to work. The time it takes to drive to work each day is independent of any other day. Suzi will work 5 days next week. c. Find the probability that Suzi will be late to work at least one day next week. d. Given that Suzi will be late to work at least one day next week, find the probability that she will be late less than three times. Suzi will work 22 days this month. She will receive a bonus if she is on time at least 20 of those days. So far this month, she has worked 16 days and been on time 15 of those days. e. Find the probability that Suzi will receive a bonus.