that the heights of students at a university follow a normal distribution with a mean of 170 cm and a standard deviation o
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- Suppose that the heights of students at a university follow a
normal distribution with amean of 170 cm and a standard deviation of 8 cm. What is theprobability that a randomly selected student is between 165 and 175 cm tall? a) 0.4117 b) 0.4714 c) 0.4417 d) 0.4471
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- Suppose students' exam scores are normally distributed with mean u = 65 and standard deviation O = =10 What proportion of the students taking the test score at most 80? O a) 0.07 O b) 0.95 O c) 0.14 d) 0.93 e) 0.99Suppose the mean weight of carryion bags has a normal distribution with a mean of 7.4 pounds, with a standard deviation 2.2 pounds. Find the probability that the mean weight of a sample of 25 bookbags will exceed 7 pounds. a. .182 b. .629 c. .572 d. None of the other 4 answers e. .818Consider a population of 800 values that are normally distributed with a mean of 80 and standard deviation of 5. What proportion of values are larger than 74? a) 0.0750 b) 0.1151 c) 0.8849 d) 0.9250
- Assume that the height of a type of tree has a normal probability distribution with a mean of 85.9 ft and a standard deviation of 9.4 ft. A tree of this type grows in my backyard and it stands 59.6 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter. My neighbor also has a tree of this type growing in her backyard, but hers stands 74.6 feet tall. Find the probability that the full height of a randomly selected tree is at least as tall as hers. Enter your answers as decimals accurate to 3 decimal places.Suppose that the middle 95% of score on a statistics final fall between 60.67 and 90.75. Give an approximate estimate of the standard deviation of scores. Assume the scores have a normal distribution. Question 7 options: 1) 15.04 2) 75.71 3) 3.76 4) -7.52 5) 7.52An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with a mean of 119 cm and a standard deviation of 5.7 cm. A. Find the probability that one selected subcomponent is longer than 121 cm. Probability = B. Find the probability that if 4 subcomponents are randomly selected, their mean length exceeds 121 cm. Probability = C. Find the probability that if 4 are randomly selected, all 4 have lengths that exceed 121 cm. Probability =
- 8) Scores on an exam have a normal distribution with a mean of 125 and a standard deviation of 19. Be sure to draw the normal distribution and shade the are being found. a) Find the probability that a person would score above 129 b) Find the probability that a person would score between 123 and 151. c) Find the probability that a group of 7 people would have a mean score above 130. d) Find the score needed to be in the top 10% of the class.Suppose that the average song length in America is 4 minutes with a standard deviation of 1.25 minutes. It is known that song length is not normally distributed. Find the probability that a single randomly selected song from the population will be longer than 4.25 minutes. Round to the nearest thousandth. a) 0.421 b) 0.079 c) 0.579 d) This probability cannot be determined because we do not know the distribution of the populationAn elevator has a placard stating that the maximum capacity is 4400 lb-29 passengers. So, 29 adult male passengers can have a mean weight of up to 4400/29 = 152 pounds. Assume that weights of males are normally distributed with a mean of 180 lb and a standard deviation of 29 lb. a. Find the probability that 1 randomly selected adult male has a weight greater than 152 lb. b. Find the probability that a sample of 29 randomly selected adult males has a mean weight greater than 152 lb. c. What do you conclude about the safety of this elevator? a. The probability that 1 randomly selected adult male has a weight greater than 152 lb is ☐ (Round to four decimal places as needed.)
- 3. Assume the heights of students at Champlain College are normally distributed with a mean of 64.0 inchesand a standard deviation of 1.2 inches. Which of the following values best approximates the probabilityof randomly selecting a Champlain College studenttallerthan 62.2 inches?A. 0.0668B. 0.0359C. 0.9332D. 0.9641E. 1.0155An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with a mean of 115 cm and a standard deviation of 5.5 cm. A. Find the probability that one selected subcomponent is longer than 117 cm. Probability = B. Find the probability that if 4 subcomponents are randomly selected, their mean length exceeds 117 cm. Probability = C. Find the probability that if 4 are randomly selected, all 4 have lengths that exceed 117 cm. Probability =5. The mean birth weight for babies born one month early is 2630 grams. Assume that the population has a standard deviation of 220 grams. Sketch the distribution of birth weights (in grams) of children born one month early. Calculate probability of a child born one month early with a birth weight between 2100 grams and 2900 grams. Find the weight which corresponds to the top 25% of birth weights for babies born one month early.