Question

Suppose a geyser has a mean time between eruptions of 100 minutes. Let the interval of time between the eruptions be normal distbuted with standard deviation 3 minutes. Complete parts (a) through ) (a) What is the probability that a randomly selected time interval between eruption is longer than 118 minutes? The probability that a randomly selected me interval is longer than 118 minutes approximately (Round to four decimal places as needed.) (6) What is the probability that a random sample of 7 time intervals between eruptions as a mean longer than 118 minutes? The probability that the mean of a random sample of 7 me intervals is more than 118 minutes is approximately (Round to four decimal places as needed) (c) What is the probability that a random sample of 23 time intervals between eruptions has a mean longer than 118 minutes? The probably the mean of a random sample of 23 metervals is more than 118 mins is proximately (Round to four decimal places as noded) (d) What efect does increasing the sample size have on the probability Provide an explanation for this in the banks below If the population mean is less than 118 minutes, then the probability that the same mean of the time between options is greater than 118 minutes because ther e in the sample mean Click to select your n e aps lock

Answer 1

a) P(X > 118)

= P((X - $\mu$ )/$\sigma$ > (118 - $\mu$ )/$\sigma$)

= P(Z > (118 - 100)/38)

= P(Z > 0.47)

= 1 - P(Z < 0.47)

= 1 - 0.6808

= 0.3192

b) P($\bar x$ > 118)

= P(($\bar x$ - $\mu$ )/($\sigma/\sqrt n$) > (118 - $\mu$ )/($\sigma/\sqrt n$))

= P(Z > (118 - 100)/(38/$\sqrt 7$))

= P(Z > 1.25)

= 1 - P(Z < 1.25)

= 1 - 0.8944

= 0.1056

c) P($\bar x$ > 118)

= P(($\bar x$ - $\mu$ )/($\sigma/\sqrt n$) > (118 - $\mu$ )/($\sigma/\sqrt n$))

= P(Z > (118 - 100)/(38/$\sqrt {23}$))

= P(Z > 2.27)

= 1 - P(Z < 2.27)

= 1 - 0.9884

= 0.0116

d) If the population mean is less than 118 minutes, then the probability that the sample mean of the time eruptions is greater than 118 minutes decreases because the variability in the sample mean increases as the sample size increases.

e) Option - A) The population mean must be more than 100, since the probability is so low.