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- Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with a mean of 160.5 ft and a standard deviation of 9.7 ft. A tree of this type grows in my backyard, and it stands 162.4 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter. P(X 169.2) = Enter your answers as decimals accurate to 4 decimal places.Assume that the weights of all packages of a certain brand of cookies are normally distrib- uted with a mean of 32 ounces and a standard deviation of .3 ounce. Find the probability that the mean weight, x, of a random sample of 20 packages of this brand of cookies will be be- tween 31.8 and 31.9 ounces.The average grade of Grade 11 students in Statistics and Probability is 85 with a standard deviation of 1.5 Solve for the probability of the following: a) The average grade is less than 88 b) The average grade is more than 88 c) The average is less than 82
- can you solve this for me by showing step by step for each question? Acme Food manufactures and sells bags of doughnuts whose weights follow a normal distribution with a mean of 400g and standard deviation 8g. a) Find the probability that a bag of doughnuts weights less than 410g b) Find P (X>412) c) Find P (395 < X < 404) d) The company can be prosecuted if the bags are less than 380g, if the company sells 50 bags per day find the expected number of bags under this weight. e) On a typical day 1.22% of bags are rejected as they are too heavy. Find the rejection weight.what is the probability that the average length of hands is less than 187 for a group of 18 men. The mean is 188 and the standard deviation is 7.1 using the central limit theoremA stick of length 1 is broken at a point chosen uniformly along its length. One piece is used as the length of a rectangle, and the other is used as the width. Find the mean area of a rectangle formed in this way.
- Suppose that a category of world-class runners are known to run a marathon (26 miles) in an average of 147 minutes with a standard deviation of 11 minutes. Consider 49 of the races. Let x̅ = the average of the 49 races. A) Give the distribution x̅ (round your standard deviation to two decimal places.) x̅~______(______,______) B) Find the probability that the average of the sample will be between 144 and 148 minutes in these 49 marathons. (Round your answer to four decimal places.) C) Find the 70th percentile for the average of these 49 marathons. (Round your answer to two decimal places.) ______ min D) Find the median of the average running times. _____minSuppose that the average height of men in the United States is approximately normallydistributed with a mean of approximately 70 inches and a standard deviation ofapproximately 4 inches. (a) If you take a sample of 4 men, find Pr {68 ≤ Y̅ ≤ 73}, the probability that the sample mean Y̅ will be between 68 and 73 inches. (b) If you take a sample of 16 men, find Pr {68 ≤ Y̅ ≤ 73}, the probability that the sample mean Y̅ will be between 68 and 73 inches. (c) If you take a sample of n men where n > 16, which one of the following is true? (circle one of the three statements.)Pr{68 ≤ Y̅ ≤ 73} > the probability that you found in (b)Pr{68 ≤ Y̅ ≤ 73} = the probability that you found in (b)Pr{68 ≤ Y̅ ≤ 73} < the probability that you found in (b)Solve it correctly
- The manager of a grocery store has selected a random sample of 100 customers. The average length of time these 100 customers to check out was 30 minutes. It is known that the mandand deviation of the checkest time is 1 minute With a 90 probability, the sample mean will provide a margin of error of 1645 10 196 1.9622pls help me and write the solution down on a paper if you can thank you
