Suppose a geyser has a mean time between eruptions of 84 minutes. let the interval of time between the eruptions be normally distributed with standard deviation 31 minutes. complete parts (a) through (e) below. (a) what is the probability that a randomly selected time interval between eruptions is longer than 99 minutes? the probability that a randomly selected time interval is longer than 99 minutes is approximately nothing. (round to four decimal places as needed.) (b) what is the probability that a random sample of 11 time intervals between eruptions has a mean longer than 99 minutes? the probability that the mean of a random sample of 11 time intervals is more than 99 minutes is approximately nothing. (round to four decimal places as needed.) (c) what is the probability that a random sample of 19 time intervals between eruptions has a mean longer than 99 minutes? the probability that the mean of a random sample of 19 time intervals is more than 99 minutes is approximately nothing. (round to four decimal places as needed.) (d) what effect does increasing the sample size have on the probability? provide an explanation for this result. fill in the blanks below. if the population mean is less than 99 minutes, then the probability that the sample mean of the time between eruptions is greater than 99 minutes ▼ increases decreases because the variability in the sample mean ▼ decreases increases a