The most famous geyser in the world, Old Faithful in Yellowstone National Park, has a mean time between eruptions of 85 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 21.25 minutes, complete parts (a) through (f). Click here to view the standard normal distribution table (page 1).LOADING... Click here to view the standard normal distribution table (page 2).LOADING... Question content area bottom Part 1 (a) What is the probability that a randomly selected time interval between eruptions is longer than 95 minutes? The probability that a randomly selected time interval is longer than 95 minutes is approximately enter your response here. (Round to four decimal places as needed.) Part 2 (b) What is the probability that a random sample of 7 time intervals between eruptions has a mean longer than 95 minutes? The probability that the mean of a random sample of 7 time intervals is more than 95 minutes is approximately enter your response here. (Round to four decimal places as needed.) Part 3 (c) What is the probability that a random sample of 22 time intervals between eruptions has a mean longer than 95 minutes? The probability that the mean of a random sample of 22 time intervals is more than 95 minutes is approximately enter your response here. (Round to four decimal places as needed.) Part 4 (d) What effect does increasing the sample size have on the probability? Provide an explanation for this result. If the sample size increases, the probability ▼ increasesincreases decreasesdecreases because the variability in the sample mean ▼ increases.increases. decreases.decreases. Part 5 (e) What might you conclude if a random sample of 22 time intervals between eruptions has a mean longer than 95 minutes? Select all that apply. A. The population mean must be more than 85 minutes, since the probability is so low. B. The population mean is 85 minutes, and this is an example of a typical sampling result. C. The population mean cannot be 85 minutes, since the probability is so low. D. The population mean is 85 minutes, and this is just a rare sampling. E. The population mean is probably less than 85 minutes. F. The population mean must be less than 85 minutes, since the probability is so low. G. The population mean is probably greater than 85 minutes.

Question

The most famous geyser in the​ world, Old Faithful in Yellowstone National​ Park, has a mean time between eruptions of 85 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 21.25 ​minutes, complete parts​ (a) through​ (f). Click here to view the standard normal distribution table (page 1).LOADING... Click here to view the standard normal distribution table (page 2).LOADING... Question content area bottom Part 1 ​(a) What is the probability that a randomly selected time interval between eruptions is longer than 95 ​minutes? The probability that a randomly selected time interval is longer than 95 minutes is approximately enter your response here. ​(Round to four decimal places as​ needed.) Part 2 ​(b) What is the probability that a random sample of 7 time intervals between eruptions has a mean longer than 95 ​minutes? The probability that the mean of a random sample of 7 time intervals is more than 95 minutes is approximately enter your response here. ​(Round to four decimal places as​ needed.) Part 3 ​(c) What is the probability that a random sample of 22 time intervals between eruptions has a mean longer than 95 ​minutes? The probability that the mean of a random sample of 22 time intervals is more than 95 minutes is approximately enter your response here. ​(Round to four decimal places as​ needed.) Part 4 ​(d) What effect does increasing the sample size have on the​ probability? Provide an explanation for this result. If the sample size​ increases, the probability ▼ increasesincreases decreasesdecreases because the variability in the sample mean ▼ increases.increases. decreases.decreases. Part 5 ​(e) What might you conclude if a random sample of 22 time intervals between eruptions has a mean longer than 95 ​minutes? Select all that apply. A. The population mean must be more than 85 ​minutes, since the probability is so low. B. The population mean is 85 ​minutes, and this is an example of a typical sampling result. C. The population mean cannot be 85 ​minutes, since the probability is so low. D. The population mean is 85 ​minutes, and this is just a rare sampling. E. The population mean is probably less than 85 minutes. F. The population mean must be less than 85 ​minutes, since the probability is so low. G. The population mean is probably greater than 85 minutes.

Accepted Answer

Given that.
 
X~N( μ , ?)
 
μ=85     , ?=21.25
 
Z-score =( x - μ )/?
 
NOTE:- According to bartleby…