According to the Chebyshev rule, at least what percentage of the observations in any data set are contained within a distance of 2 standard deviations around the mean? O A. 75% O a. 6m 0 c. 88.89% 0 D. 95% According to the Chebyshev rule, at least what percentage of the observations in any data set are contained within a distance of 3 standard deviations around the mean? 0 A. 95% O B. 75% O c. 33.39% 0 D. 67% Given a normal distribution with p 2109 and 0 =19, complete parts {a} through {d}. a. What is the probability that X > 85'? The probability that X a 85 is D. (Round to four decimal places as needed.) b. What is the probability that X 125? The probability that X =: 95 or X > 125 is D. (Round to four decimal places as needed.) :1. 99% of the values are between what two X-yalues (symmetrically distributed around the mean)? 99% of the values are greater than D and less than D. (Round to two decimal places as needed.) Doggie Nuggets Inc. (DNI) sells large bags of dog food to warehouse clubs. DNI uses an automatic lling process to ll the bags. Weights of the lled bags are approximately normally distributed with a mean of 64 kilograms and a standard deviation of 1.86 kilograms. Complete parts a through d below. a. What is the probability that a lled bag will weigh less than 63.6 kilograms? The probability is _ (Round to four decimal places as needed ) Aprivate equity rm is evaluating two alternative investments. Although the returns are random, each investment's return can be described using a normal distribution, The rst investment has a mean return of $2,250,000 with a standard deviation of $125,000 The second investment has a mean return of $2,425,000 with a standard deviation of $300,000. Complete parts a through :3 below. a. How likely is it tha the rst investrnentwill return $2,100,000 or less? The probability is _ (Round to four decimal places as needed.) Abottling plant fills 12-ounce cans of soda by an automated lling process that can be adjusted to any mean ll volume and that will ll cans according to a normal distribution. However, not all cans will contain the same volume due to variation in the lling process Historical records show that regardless ofwhat the mean is set at, the standard deviation in ll will be 0.095 ounce. Operations managers at the plant know that if they put too much soda in a can, the company loses money. lftoo little is put in the can. customers are short changed, and the State Department of Weights and Measures may ne the company. Complete parts a and b below. a. Suppose the industry standards for ll volume call for each 12ounce can to contain between 11.91 and 12.09 ounces. Assuming that the manager sets the mean ll at 12 ounces, what is the probability that a can will contain a volume of product that falls in the desired range? The probability is . (Round to four decimal places as needed )