A particularly long traffic light on your morning commute is green 17% of the time that you approach it. Assume that each morning represents an independent trial. Over 20 mornings, what is the probability that the light is green on exactly 4 day

Step-by-step explanation:

Assuming that we are only trying to calculate the probability of the light being green ONLY on day 4 then it would be the exact same probability as every other day, which would be 17%. Now if we are trying to calculate the probability of the light being green on the first consecutive 4 days then we would need to multiply this probability (in decimal form) four times for the four days like so...

0.17 * 0.17 * 0.17 * 0.17 = x

0.00083521 = x   ... times by 100 to get percentage

0.00083521 * 100 = 0.0835%

So the probability of the light being green 4 days in a row during your commute is 0.0835%

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).