2. It is known that the amount of time needed to change the oil on a car is normally distributed with a standard deviation of 5 minutes. A random sample of 14 cars was taken and the time taken to change the oil are measured as in Table 1. Table 1 41 72 81 87 33 58 60 69 71 108 72 72 91 82 (i) Identify the variable involved. (ii) Find a 99% confidence interval for average time taken to change the oil on cars. Give comment on the parameter estimate. (iii) Identify the estimator used in (ii). (iv) Calculate the estimation error of the confidence interval in (ii). (v) What is the effect of estimation error calculated in (iv) if the sample size increases?

Suppose that the daily intake of an adult follows a uniform distribution from 40 to 65 micrograms. Suppose that 36 adults are randomly selected. What is the mean and standard deviation of the average intake for 36 adults. a. Mean= 52.5 stvdev = 1.2 b. Mean = 55 stvdev= 7.22c. Mean = 52.5 stvdev = 2.08 d. Mean= 52.5 stvdev = 7.22

Suppose that water usages in American showers are normally distributed, with an average shower using 20 gallons, and a standard deviation of 3.2 gallons. Estimate the percentage of showers that used (a) between 13.6 and 26.4 gallons. % (b) more than 26.4 gallons. % (c) less than 10.4 gallons. % (d) between 16.8 and 29.6 gallons. %

On average, a banana will last 6.3 days from the time it is purchased in the store to the time it is too rotten to eat. The standard deviation is 2.1 days. Will the average banana spoil earlier if the banana is hung from the ceiling? The data show results of an experiment with 16 bananas that are hung from the ceiling. Assume that that distribution of the population is normal. 5, 8, 5, 7, 4, 4, 6, 8, 6, 7, 5, 7, 6, 3, 6,2 What can be concluded at the 0.10 level of significance? H0:  = 6.3 Ha: [ Select ] [">", "<", "Not Equal To"] 6.3 Test statistic:[ Select ]  ["T", "Z"]            p-Value = [ Select ] ["0.02", "0.08", "0.04", "0.16"]            [ Select ]  ["Reject Ho", "Fail to Reject Ho"]            Conclusion: There is [ Select ] ["insufficient", "statistically significant"]          evidence to make the conclusion that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is less than 6.3 days.

On a measure of running speed on a 100 meter dash, students received timed scores ranging from 12 seconds to 24 seconds. The distribution of running times is normative with a mean of 16 seconds. Transferring this ratio data to standard scores for comparison with the results of classes from other departments, the mean score is assigned a standard score of 100 with a standard deviation of 10. From this example, a standard score of 99 would mean the actual value in seconds for an individual would be about a. 16 b. 12 c. 19 d. 24

The breaking strengths of cables produced by a certain manufacturer have historically had a mean of 1775 pounds and a standard deviation of 70 pounds. The Español company believes that, due to an improvement in the manufacturing process, the mean breaking strength, µ, of the cables is now greater than 1775 pounds. To see if this is the case, 16 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1806 pounds. Assume that the population is normally distributed. Can we support, at the 0.10 level of significance, the claim that the population mean breaking strength of the newly- manufactured cables is greater than 1775 pounds? Assume that the population standard deviation has not changed. Perform a one-tailed test. Then complete the parts below. 00 Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H,…

In a certain country the heights of adult men are normally distributed with a mean of 70.2 inches and a standard deviation of 2.7 inches. The​ country's military requires that men have heights between 66 inches and 79 inches. Determine what percentage of this​ country's men are eligible for the military based on height. The percentage of men that are eligible for the military based on height is nothing​%. ​(Round to two decimal places as​ needed.)

Rhys is a quality control manager at a facility that manufactures snack foods. He is interested in the number of whole mini- pretzels that are in the 10 oz bags in the latest lot produced. Rhys selects 24 bags of mini-pretzels at random from the latest lot and counts the number of pretzels in each bag His sample has a mean of 158 pretzels with a standard deviation of 1.6 pretzels. What is the margin of error with 95% confidence (2 = 2.07)? O 0.02 O 66.76 O 0.68 O 6.34

Twelve samples of coal from a Northern Appalachian source had an average mercury content of 0.253 ppm with a standard deviation of 0.029 ppm. Suppose the density of mercury content of coal from this source is approximately normally distributed.  a.  Find the LOWER bound of a 95% confidence interval for the mean mercury content of coal from this source. b.  Find the UPPER bound of a 95% confidence for the mean mercury content of coal from this source.