Arrivals of customers at a checkout counter follow a poisson distribution. it is known that, during a given 30-minute period, one customer arrived at the counter. then the actual time of arrival follows a uniform distribution over the interval of (0, 30). find the conditional probability that a customer arrives during the last 5 minutes of the 30-minute period if it is known that no one arrives during the first 10 minutes of the period.

1/4

Step-by-step explanation:

Let X be the time of arrival measured from the beginning of the 30-minute period.

Since the number of arrivals is Poisson, the time of the arrival is equally likely in any subinterval of time of a given size in the 30 minutes, and thus X has a uniform distribution in (0,30) and P(X > 25) =

where a = 30 and b = 25

Solving, we obtain P(X > 25) = 1/6

similarly, P(X>10) = 2/3 by substituting b for 10

Hence, for conditional probability we have

P(X>25 | X>10) = P(X>25) / P(X>10) = (1/6) / (2/3) = 1/4

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.

the reporter's right

step-by-step explanation:

1/4 = .25 / 25%