Question

op Suppose a geyser has a mean time between eruptions of 61 minutes. Let the interval of time between the eruptions be normaly distributed with standard deviation 24 minutes. Complete parts (a) through le) below (a) What is the probability that a randomly selected time interval between eruptions is longer than 71 minutes? The probability that a randomly selected time interval is longer than 71 minutes is approximately (Round to four decimal places as needed (b) What is the probability that a random sample of 10 time intervals between eruptions has a mean longer than 71 minutes? The probability that the mean of a random sample of 10 time intervals is more than 71 minutes is approximately (Round to four decimal places as needed.) (e) What is the probability that a random sample of 35 time intervals between eruptions has a mean longer than 71 minutes? The probability that the mean of a random sample of 35 time intervals is more than 71 minutes is approximately (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. Fal in the blanks below of the population mean is less than 71 minutes, then the probability that the sample mean of the time between eruptions is greater than 71 minutes because the variability in the sample mean as the sample size (6) What might you conclude il a random sample of time intervals between eruptions has a mean longer than 71 minutes? Select at that apply A The population mean may be greater than 61 B. The population mean cannot be 61, since the probability is so low. C. The population mean may be less than 61 D. The population mean is 61, and this is just a rare sampling E. The population mean is 61, and this is an example of a typical sampling result OF The population mean must be more than 61, since the probability is to low. G. The population mean must be less than 61, since the probability is so low. Click to select your answers

Answer 1

(a)

x	71
n	1
mu	61
s	24
se	24
z	0.416667
p-value	0.3385

(b)

x	71
n	10
mu	61
s	24
se	7.589466
z	1.317616
p-value	0.0938

(c)

x	71
n	35
mu	61
s	24
se	4.05674
z	2.465033
p-value	0.0069

(d) decreases, decreases, increases

(e) Option A, F