Final answer:
The probability that the time between the arrivals of two customers will be less than 38 seconds is 0.6333. The probability that the time between the arrivals of two customers will be between 10 and 35 seconds is 0.4167. The probability that the time between the arrivals of two customers will be greater than 48 seconds is 0.2. The mean of the time between the arrival of two customers is 30 seconds and the standard deviation is approximately 17.32 seconds.
Step-by-step explanation:
a. The probability that the time between the arrivals of two customers will be less than 38 seconds can be found by calculating the proportion of the total time interval (60 seconds) that falls within the range of less than 38 seconds. In this case, the probability is equal to 38/60 or 0.6333.
b. To find the probability that the time between the arrivals of two customers will be between 10 and 35 seconds, we need to calculate the proportion of the total time interval (60 seconds) that falls within this range. Subtracting the probability of the lower bound from the probability of the upper bound gives us 35/60 - 10/60 = 25/60 or 0.4167.
c. The probability that the time between the arrivals of two customers will be greater than 48 seconds can be found by subtracting the probability of the lower bound (48/60) from 1. 1 - 48/60 = 12/60 or 0.2.
d. The mean of the time between the arrival of two customers can be calculated by taking the average of the upper and lower bounds of the time interval, which is (60 + 0) / 2 = 30 seconds. The standard deviation can be calculated using the formula sqrt((upper bound - lower bound)^2 / 12), which in this case is sqrt((60 - 0)^2 / 12) = sqrt(3600 / 12) = sqrt(300) ≈ 17.32 seconds.