In an effort to cut costs and improve profits, any US companies have been turning to outsourcing. In fact, according to Purchasing magazine, $54 \%$ of companies surveyed outsourced some part of their manufacturing process in the past two to three years. Suppose 555 of these companies are contacted. b. What is the probability percentage that 285 or more companies outsourced some part of their manufacturing process in the past two or three years? Round the percent to two decimal places. c. What is the probability percentage that $48 \%$ or less of these companies outsourced some part of their manufacturing process in the past two or three years? Round the percent to two decimal places.

Step 1 ：Given that 54% of companies surveyed outsourced some part of their manufacturing process in the past two to three years, we are asked to find the probability that 285 or more companies out of 555 surveyed companies outsourced some part of their manufacturing process in the past two to three years.

Step 2 ：We can model this situation using a binomial distribution with parameters \(n = 555\) (the number of trials) and \(p = 0.54\) (the probability of success on each trial).

Step 3 ：The probability that 285 or more companies outsourced some part of their manufacturing process in the past two to three years is given by \(1 - P(X < 285)\), where \(X\) is a random variable following the binomial distribution with parameters \(n\) and \(p\).

Step 4 ：Calculating this probability gives approximately 0.902 or 90.2%.

Step 5 ：We are also asked to find the probability that 48% or less of these companies outsourced some part of their manufacturing process in the past two to three years.

Step 6 ：This is equivalent to finding the probability that 266 or fewer companies outsourced some part of their manufacturing process, as \(48\%\) of 555 is approximately 266.

Step 7 ：This probability is given by \(P(X \leq 266)\), where \(X\) is a random variable following the binomial distribution with parameters \(n\) and \(p\).

Step 8 ：Calculating this probability gives approximately 0.0024 or 0.24%.

Step 9 ：Final Answer: The probability that 285 or more companies outsourced some part of their manufacturing process in the past two to three years is approximately \(\boxed{90.2\%}\). The probability that 48% or less of these companies outsourced some part of their manufacturing process in the past two to three years is approximately \(\boxed{0.24\%}\).