Given a normal distribution with p = 100 and o = 10, complete parts (a) through (d). <:> a. What is the probability that X > 85? The probability that x > 85 is D. (Round to four decimal places as needed.) b. What is the probability that X 105? The probability that x 105 is D. (Round to four decimal places as needed.) d. 99% of the values are between what two X-values (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 filling process to fill the bags. Weights of the filled bags are approximately normally distributed with a mean of 52 kilograms and a standard deviation of 0.77 kilograms. Complete parts a through d below. . . . a. What is the probability that a filled bag will weigh less than 51.3 kilograms? The probability is (Round to four decimal places as needed.)Doggie Nuggets Inc. (DNI) sells large bags of dog food to warehouse clubs. DNI uses an automatic filling process to fill the bags. Weights of the filled bags are approximately normally distributed with a mean of 52 kilograms and a standard deviation of 0.77 kilograms. Complete parts a through d below. . . . a. What is the probability that a filled bag will weigh less than 51.3 kilograms? The probability is (Round to four decimal places as needed.)A private 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 $2,000,000 with a standard deviation of $175,000. The second investment has a mean return of $2,225,000 with a standard deviation of $400,000. Complete parts a through c below. E) a. How likely is it that the rst investment will return $1 ,700,000 or less? The probability is D. (Round to four decimal places as needed.) A bottling plant lls 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 of what the mean is set at, the standard deviation in ll will be 0.035 ounce. Operations managers at the plant know that if they put too much soda in a can, the company loses money. If too 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. E> a. Suppose the industry standards for ll volume call for each 12-ounce can to contain between 11.96 and 12.04 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 D. (Round to four decimal places as needed.) The annual per capita consumption of bottled water was 32.9 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 32.9 and a standard deviation of 12 gallons. a. What is the probability that someone consumed more than 43 gallons of bottled water? b. What is the probability that someone consumed between 25 and 35 gallons of bottled water? 0. What is the probability that someone consumed less than 25 gallons of bottled water? d. 95% of people consumed less than how many gallons of bottled water? Atrucking company determined that the distance traveled per truck per year is normally distributed, with a mean of 70 thousand miles and a standard deviation of 11 thousand miles. Complete parts (a) through (c) below. E) a. What proportion of trucks can be expected to travel between 56 and 70 thousand miles in a year? The proportion of trucks that can be expected to travel between 56 and 70 thousand miles in a year is El. (Round to four decimal places as needed.) A set of nal examination grades in an introductory statistics course is normally distributed, with a mean of 76 and a standard deviation of 7. Complete parts (a) through (d). E) .a. What is the probability that a student scored below 87 on this exam? The probability that a student scored below 87 is 0.9420 . (Round to four decimal places as needed.) b. What is the probability that a student scored between 69 and 91? The probability that a student scored between 69 and 91 is D. (Round to four decimal places as needed.) A study indicates that 18- to 24- year olds spend a mean of 115 minutes watching video on their smartphones per month. Assume that the amount of time watching video on a smartphone per month is normally distributed and that the standard deviation is 20 minutes. Complete parts (a) through (d) below. <:> a. What is the probability that an 18- to 24-year-old spends less than 90 minutes watching video on his or her smartphone per month? The probability that an 18- to 24-year-old spends less than 90 minutes watching video on his or her smartphone per month is 0.1056 . (Round to four decimal places as needed.) b. What is the probability that an 18- to 24-year-old spends between 90 and 155 minutes watching video on his or her smartphone per month? The probability that an 18- to 24-year-old spends between 90 and 155 minutes watching video on his or her smartphone per month is D. (Round to four decimal places as needed.) A survey found that women's heights are normally distributed with mean 62.4 in. and standard deviation 3.6 in. The survey also found that men's heights are normally distributed with mean 69.4 in. and standard deviation 3.5 in. Consider an executive jet that seats six with a doonlvay height of 56.4 in. Complete parts (a) through (c) below. E) a. What percentage of adult men can t through the door without bending? The percentage of men who can t without bending is 0.00 %. (Round to two decimal places as needed.) b. Does the door design with a height of 56.4 in. appear to be adequate? Why didn't the engineers design a larger door? A. The door design is inadequate, because every person needs to be able to get into the aircraft without bending. There is no reason why this should not be implemented. B. The door design is adequate, because the majority of people will be able to t without bending. Thus, a larger door is not needed. 3 C. The door design is inadequate, but because the jet is relatively small and seats only six people, a much higher door would require major changes in the design and cost of the jet, making a larger height not practical. D. The door design is adequate, because although many men will not be able to t without bending, most women will be able to t without bending. Thus, a larger door is not needed. c. What doorway height would allow 40% of men to t without bending? The doonNay height that would allow 40% of men to t without bending is D in. (Round to one decimal place as needed.) Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1), determine the following probabilities. a. P(Z> 1.09) b. P(Z 1.09) = 0.1379 (Round to four decimal places as needed.) b. P(Z