In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and '10 represents the best possible lite. The responses were normally distributed, with a mean of 5.3 and a standard deviation of 2.2. Answer parts (aHd} below. ..... ) (a) Find the probability that a randomly selected study participants response was less than 4. The probability that a randomly selected study participant's response was less than 4 is D. [Round to four decimal places as needed.) (b) Find the probability that a randomly selected study participants response was between 4 and B. The probability that a randomly selected study participant's response was between 4 and B is . (Round to four decimal places as needed.) {c} Find the probability that a randomly selected study participant's response was more than 8. The probability that a randomly selected study participant's response was more than B is D. {Round to tour decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. 0 A. The events in parts {a} and (c) are unusual because their probabilities are less than 0.05. (E! B. The event in part {a} is unusual because its probability is less than 0.05. O C. The events in parts (a), (b), and {c} are unusual because all of their probabilities are less than 0.05. O D. There are no unusual events because all the probabilities are greater than 0.05. In a survey of a group of men, the heights in the 2029 age group were nonhally distributed, with a mean oi 5?.1 inches and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than 65 inches. The probability that the study participant selected at random is less than E35 inches tail is El. (Round to four decimal places as needed.) (b) Find the probability that a study participant has a height that is between 85 and ?1 inches. The probability that the study participant selected at random is between 65 and 71 inches tail is El. (Round to four decimal places as needed.) (cl Find the probability that a study participant has a height that is more than T1 inches. The probability that the study participant selected at random is more than 71 inches tail is |:. (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. 0 A. The events in parts {a} and (c) are unusual because its probabilities are less than 0.05. O B. There are no unusual events because all the probabilities are greater than 0.05. O C. The events in parts {a}, (b), and {c} are unusual because all of their probabilities are less than 0.05. O D. The event in part {a} is unusual because its probability is less than 0.05. Use the standard normal table to nd the zscore that corresponds to the given percentile. If the area is not in the table, use the entry closest to the area. lithe area is halfwayr between two entries, use the zscore halfway between the corresponding zscores. If convenient. use technology to nd the zscore. P4 Click to View page 1 of the table. Click to view page 2 ofthe table. The zscore that corresponds to P4 is D. (Round to two decimal places as needed.) A gear has been designed to have a diameter of 4 inches. The standard Is the process in control or out of control? Select all that apply. deviation of the process is 0.5 inch. A control chart is shown. Each chart has horizontal lines drawn at the mean, p, u+20, and at u + 30. Determine if the A. Out of control, because two out of three consecutive points lie process shown is in control or out of control. Explain. more than two standard deviations from the mean. Gears OB. Out of control, because there are nine consecutive points either above or below the mean. C. Out of control, because a point lies more than three standard deviations beyond the mean. Diameter (inches) D. In control, because none of the three warning signals detected a change. 3 5 6 7 8 9 10 11 Observation numberAssume the random variable x is normally distributed with mean u =8? and standard deviation 0' =5. Find the indicated probability. PD: