Healty people have body temperatures that are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F . (a) If a healthy person is randomly selected, what is the probability that he or she has a temperature above 99.4°F? answer: (b) A hospital wants to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only 0.5 % of healty people to exceed it? answer:
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- You are planning a May camping trip to Denali National Park in Alaska and want to make sure your sleeping bag is warm enough. The average low temperature in the park for May follows a normal distribution with a mean of 32°F and a standard deviation of 8°F. One sleeping bag you are considering advertises that it is good for temperatures down to 25°F. What is the probability that this bag will be warm enough on a randomly selected May night at the park?Show neat and complete solution. (... The average fuel efficiency of U.S. light vehicles (cars, SUVs, minivans, vans, and light trucks) for 2005 was 21 miles per gallon (mpg). If the standard deviation of the population was 2.8 and the gas ratings were normally distributed, (a) what is the probability that the mean mpg for a random sample of 25 light vehicles is under 18? (b) between 20 and 24? Given: Required: Solution: a. b.Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 65 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ? = 65 tons and standard deviation ? = 1.7 ton. (a) What is the probability that one car chosen at random will have less than 64.5 tons of coal? (Round your answer to four decimal places.)(b) What is the probability that 37 cars chosen at random will have a mean load weight x of less than 64.5 tons of coal? (Round your answer to four decimal places.)
- Women's shoe sizes are (approximately) normally distributed, with an average size of 8.076 and a standard deviation of 1.468. You work at Vogue Magazine, and would like to interview some women about how shoes fit. You take a random sample of 10 women. What is the probability that the 10 women you sampled had an average shoe size that is less than 8?What are the class boundaries for the class limit, 2.20 - 3.80 ? 2.15 - 3.75 2.195 - 3.805 2.395 - 3.805 1.7 - 4.215. You have a box of winter accessories in your attic with 12 hats and 23 scarves. A. Construct a tree diagram to model possible outcomes and probabilities in which you draw two accessories without replacement. B. Find the probability of getting two scarves. C. Find the probability of getting a hate first and a scarf second.
- The fill amount of bottles of a soft drink is normally distributed, with a mean of 2.0 liters and a standard deviation of 0.10 liter. If you select a random sample of 100 bottles, a. what is the probability that the sample mean will be between 1.98 and 2.02 liters? b. what is the probability that the sample mean will be below 1.99 liters? c. what is the probability that the sample mean will be greater than 2.02 liters? d. The probability is 95% that the sample mean amount of soft drink will be at least how many liters?Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 62 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ? = 62 tons and standard deviation ? = 0.5 ton. (a) What is the probability that one car chosen at random will have less than 61.5 tons of coal? (Round your answer to four decimal places.)(b) What is the probability that 45 cars chosen at random will have a mean load weight x of less than 61.5 tons of coal? (Round your answer to four decimal places.)(c) Suppose the weight of coal in one car was less than 61.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? YesNo Suppose the weight of coal in 45 cars selected at random had an average x of less than 61.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why? Yes, the probability that this…Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 74 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ? = 74 tons and standard deviation ? = 1.9 ton. (a) What is the probability that one car chosen at random will have less than 73.5 tons of coal? (Round your answer to four decimal places.)(b) What is the probability that 50 cars chosen at random will have a mean load weight x of less than 73.5 tons of coal? (Round your answer to four decimal places.)
- Suppose that the lifetimes of light bulbs are approximately normally distributed, with a mean of 57 hours and a standard deviation of 3.5 hours. With this information, answer the following questions. (a) What proportion of light bulbs will last more than 62 hours? (b) What proportion of light bulbs will last 52 hours or less? (c) What proportion of light bulbs will last between 59 and 62 hours? (d) What is the probability that a randomly selected light bulb lasts less than 45 hours?Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The automatic hopper car loader is set to put 69 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean ? = 69 tons and standard deviation ? = 1.5 ton. (a) What is the probability that one car chosen at random will have less than 68.5 tons of coal? (Round your answer to four decimal places.)(b) What is the probability that 46 cars chosen at random will have a mean load weight x of less than 68.5 tons of coal? (Round your answer to four decimal places.)(c) Suppose the weight of coal in one car was less than 68.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? YesNo Suppose the weight of coal in 46 cars selected at random had an average x of less than 68.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why? Yes, the probability that this…Suppose that the lifetimes of light bulbs are approximately normally distributed, with a mean of 57 hours and a standard deviation of 3.5 hours. With this information, answer the following questions. (a) What proportion of light bulbs will last more than 60 hours? (b) What proportion of light bulbs will last 50 hours or less? (c) What proportion of light bulbs will last between 58 and 61 hours? (d) What is the probability that a randomly selected light bulb lasts less than 46 hours? (a) The proportion of light bulbs that last more than 60 hours is (Round to four decimal places as needed.) (b) The proportion of light bulbs that last 50 hours or less is (Round to four decimal places as needed.) (c) The proportion of light bulbs that lasts between 58 and 61 hours is (Round to four decimal places as needed.)