Question

Suppose a geyser has a mean time between eruptions of 95 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 27 minutes, answer the following questions a) What is the probability that a randomly selected time interval between eruption is longer than 10 minutes? The probability that a randomly selected time interval is longer than 106 minutes is approximately Round to four decimal places as needed) (b) What is the probability that a random sample of 13 time intervals between eruptions has a mean longer than 106 minutes? The probability that the mean of a random sample of 13 time intervals is more than 106 minutes is approximately (Round to four decimal places as needed) (e) What is the probability that a random sample of 38 me intervals between eruptions has a mean longer than 106 minutes? The probability that the mean of a random sample of 38 time intervals is more than 106 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 res. Choose the correct answer below. O A The probability decreases because the variability in the sample mean increases as the sample size increases OB. The probability increases because the variability in the sample mean decreases as the sample size increases OC. The probability increases because the variability in the sample mean increases as the sample size increases D. The probability decreases because the variability in the sample mean decreases as the sample size increases le) What might you conclude a random sample of 38 me interval between ons has a mean longer than 106 minutes? Choose the best answer below O A The population mean is 95 minutes, and this is an example of a typical sampling, OB. The population mean may be greater than 95 OC. The population mean must be more than 95 in the probability is so low D. The population mean cannot be 95, since the probability is so low Click to select your answers

Answer 1

I sol M=95, re 27 I (a) PI longer than 106) P(x >106 ) = P(Z > Yodey - = f(z> 106.795) . 106-95 27 = P(Z > 0.4074) = 0.3419 or 0.3409 - Tey both (6) Pllonger than 106), n=13 PER > 106) = P(Z > Ballons = P(Z > 106-15 2 = P(Z > 1.4689 ) = 0.0709. of 0.0708 by both csscanned with CamScanner

(C) Pllonger than 100), n = 38 PLX 3100) = P(Z > Kereta =P[z> hit = P(Z > 2.5114) = 0.0060 1 (d) option (D) ce) option (D) CSScanned with CamScanner