Question

an employee at shell gas station has determined that only 3% of customers purchase gold grade gasoline. let x be the number of customers one day until the first person buys gold grade gasoline. what is p (10 < x < 25)?

Answer 1

The probability that it takes between 10 and 25 customers until the first person buys gold grade gasoline can be calculated using the complement rule.

Step-by-step explanation:

The probability that a customer purchases gold grade gasoline is 3%, which means the probability that a customer does not purchase gold grade gasoline is 97%.

Let's define the event A as the event that a customer purchases gold grade gasoline. We can use the complement rule to find the probability that it takes between 10 and 25 customers until the first person buys gold grade gasoline.

P(10 < x < 25) = P(x ≥ 10) - P(x ≥ 25)

P(x ≥ 10) = P(not A) * P(not A) * ... * P(not A) * P(A) = (0.97)^9 * 0.03

P(x ≥ 25) = P(not A) * P(not A) * ... * P(not A) = (0.97)^24

Therefore, P(10 < x < 25) = (0.97)^9 * 0.03 - (0.97)^24