Consider babies born in the "normal" range of 37-43 weeks gestational age. A paper suggests that a normal distribution with mean μ = 3,500 grams and standard deviation o = 675 grams is a reasonable model for the probability distribution of the continuous numerical variable x = birth weight of a randomly selected full-term baby. USE SALT (a) What is the probability that the birth weight of a randomly selected full-term baby exceeds 4,000 g? (Round your answer to four decimal places.) 0.2451 X (b) What is the probability that the birth weight of a randomly selected full-term baby is between 3,000 and 4,000 g? (Round your answer to four decimal places.) (c) What is the probability that the birth weight of a randomly selected full-term baby is either less than 2,000 g or greater than 5,000 g? (Round your answer to four decimal places.)

The height of American men in feet is modeled with a normal distribution, with mean μ = 5.75 feet and variance o² = 0.333 feet. What is the probability that a randomly selected man's height is between 6 and 6.5 feet? Round to the nearest 4th decimal place, 0.xxxx

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 70 tons of coal into each car. The actual weights of coal loaded into each car are normally distributed, with mean u = 70 tons and standard deviation o = 1.4 ton. n USE SALT (a) What is the probability that one car chosen at random will have less than 69.5 tons of coal? (Round your answer to four decimal places.) (b) What is the probability that 30 cars chosen at random will have a mean load weight x of less than 69.5 tons of coal? (Round your answer to four decimal places.) (c) Suppose the weight of coal in one car was less than 69.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? O Yes O No Suppose the weight of coal in 30 cars selected at random had an average x of less than 69.5 tons. Would that fact make you suspect that the loader had slipped out of adjustment? Why? O Yes, the probability that…

If XX represents a random variable coming from a normal distribution and P(X<10.2)=0.22P(X<10.2)=0.22, then P(X>10.2)=0.78P(X>10.2)=0.78.   true or false