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.\[ P(X < 162.4) = \]My neighbor also has a tree of this type growing in her backyard, but hers stands 169.2 feet tall. Find the probability that the full height of a randomly selected tree is at least as tall as hers.\[ P(X > 169.2) = \]Enter your answers as decimals accurate to 4 decimal places.

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Answered: Let X represent the full height of a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Dandelions are studied for their effects on crop production and lawn growth. In one region, the mean number of dandelions per square meter was found to be 8. Find the probability of no dandelions in an area of 1 m². P(X= 0): = Find the probability of at least one dandelion in an area of 1 m². P(at least one) = Find the probability of at most two dandelions in an area of 1 m². P(X ≤ 2)
Assume that the amount of weight that male college students gain during their freshman year are normally distributed with a. Mean of u= 1.2 kg and a standard deviation of o= 5.1 kg A. If 1 male college student is randomly selected, Find the probability that he gains between 0 and 3 kg during freshman year B. If 25 male college students are randomly selected find the probability that their mean weight gain during freshman year is between 0 and 3 kg why can the normal distribution be used on pet b even though the sample size does not exceed 30?
An 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 =
Two devices are used to measure the length of beam. If the true length of the beam is L, the measurement error made by one device, E, , is normally distributed with mean 0 and standard deviation 0.006L, and the measurement error made by the other device, E, , is normally distributed with mean 0 and standard deviation 0.004L. The two measurement errors are independent of each other. What is the probability that the average value of the two measurements, (E, + E,)/2, is within 0.5% of L? Note that this problem can be done using the attached table of the cdf of the standard normal random variable.
An 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.)
The average age of all employees is 25 years, and the standard deviation of the ages of all employees is 3 years. Suppose 100 employees are randomly selected.
The number of feathers on a typical blue jay is believed to be normally distributed. On average, it is know that a blue jay will have 200 feathers and with a standard deviation of 10. The probability that the mean of 25 randomly selected blue jays will be between 185 and 202 feathers is equivalent to: O a. P(-15
A randomly selected group of 560 students are assumed to have heights distributed normally with meanµ = 166 cm and standard deviation σ = 30 cm. Suppose a student is chosen randomly from this group. Finda. the probability that this student’s height is between 170 cm and 182 cm.b. the probability that this student’s height is bigger than 175 cm.
Assume that women's heights are normally distributed with a mean 64.5 in, and a standard deviation of 2.3 in. (a) if 1 woman is randomly selected, find the probability that her height is less than 65 in.(b) if 46 women are randomly selected, find the probability that they have a mean height less than 65 in.
Assume that the readings at freezing on a bundle of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading greater than -1.935°C.
An 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 =
An elevator has a placard stating that the maximum capacity is 4100 lb-27 passengers. So, 27 adult male passengers can have a mean weight of up to 4100/27= 152 pounds. Assume that weights of males are normally distributed with a mean of 185 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 27 randomly selected adult males has a mean weight greater than 152 lb. c. What do you conclude about the safety of this elevator? Round to four decimal places as needed

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