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An experiment investigated whether the stem diameters of a tulip would change depending on whether the plant was left swinging freely in the wind or was artificially supported. Suppose that the unsupported stem diameters of the tulip plant have a normal distribution with an average diameter of 25 mm(millimetres) and a standard deviation of 2 mm. a) If two tulip plants are randomly selected, what is the probability that both plants will have a stem diameter of more than 28 mm? b) Suppose the papulation mean of unsupported stem diameter of the tulip plant is unknown with a standard deviation of 2 mm, and the probability that unsupported stem diameter of the tulip plant is more than 22 mm is 99%. Calculate the population mean of unsupported stem diameter of the tulip plant. c) It is known from historical records that the proportion of artificially supported tulip plants that have a stem diameter change is forty two percent. If a sample of 140 artificially supported tulip plants are selected at random, what is the probability that more than thirty percent of the artificially supported tulip plants are with a changed diameter?

An experiment investigated whether the stem diameters of a tulip would change depending on whether the plant was left swinging freely in the wind or was artificially supported. Suppose that the unsupported stem diameters of the tulip plant have a normal distribution with an average diameter of 25 mm(millimetres) and a standard deviation of 2 mm. a) If two tulip plants are randomly selected, what is the probability that both plants will have a stem diameter of more than 28 mm? b) Suppose the papulation mean of unsupported stem diameter of the tulip plant is unknown with a standard deviation of 2 mm, and the probability that unsupported stem diameter of the tulip plant is more than 22 mm is 99%. Calculate the population mean of unsupported stem diameter of the tulip plant. c) It is known from historical records that the proportion of artificially supported tulip plants that have a stem diameter change is forty two percent. If a sample of 140 artificially supported tulip plants are selected at random, what is the probability that more than thirty percent of the artificially supported tulip plants are with a changed diameter?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 14PPS
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An experiment investigated whether the stem diameters of a tulip would change depending on whether the plant was left swinging freely in the wind or was artificially supported. Suppose that the unsupported stem diameters of the tulip plant have a normal distribution with an average diameter of 25 mm(millimetres) and a standard deviation of 2 mm. a) If two tulip plants are randomly selected, what is the probability that both plants will have a stem diameter of more than 28 mm? b) Suppose the papulation mean of unsupported stem diameter of the tulip plant is unknown with a standard deviation of 2 mm, and the probability that unsupported stem diameter of the tulip plant is more than 22 mm is 99%. Calculate the population mean of unsupported stem diameter of the tulip plant. c) It is known from historical records that the proportion of artificially supported tulip plants that have a stem diameter change is forty two percent. If a sample of 140 artificially supported tulip plants are selected at random, what is the probability that more than thirty percent of the artificially supported tulip plants are with a changed diameter? d) Another experiment was also conducted in another journal. Suppose that the unsupported stem diameters of the tulip plants are normally distributed with an average diameter of 25 mm (millimetres) and a standard deviation of 2 mm, while artificially supported stem diameters of the tulip plants are normally distributed with an average diameter of 28 mm and a standard deviation of 3 mm. What is the probability that the average diameter of 6 randomly selected unsupported stems of tulip plants is 1 mm wider than the average diameter of 4 randomly selected artificially supported stems of tulip plants?
Transcribed Image Text:An experiment investigated whether the stem diameters of a tulip would change depending on whether the plant was left swinging freely in the wind or was artificially supported. Suppose that the unsupported stem diameters of the tulip plant have a normal distribution with an average diameter of 25 mm(millimetres) and a standard deviation of 2 mm. a) If two tulip plants are randomly selected, what is the probability that both plants will have a stem diameter of more than 28 mm? b) Suppose the papulation mean of unsupported stem diameter of the tulip plant is unknown with a standard deviation of 2 mm, and the probability that unsupported stem diameter of the tulip plant is more than 22 mm is 99%. Calculate the population mean of unsupported stem diameter of the tulip plant. c) It is known from historical records that the proportion of artificially supported tulip plants that have a stem diameter change is forty two percent. If a sample of 140 artificially supported tulip plants are selected at random, what is the probability that more than thirty percent of the artificially supported tulip plants are with a changed diameter? d) Another experiment was also conducted in another journal. Suppose that the unsupported stem diameters of the tulip plants are normally distributed with an average diameter of 25 mm (millimetres) and a standard deviation of 2 mm, while artificially supported stem diameters of the tulip plants are normally distributed with an average diameter of 28 mm and a standard deviation of 3 mm. What is the probability that the average diameter of 6 randomly selected unsupported stems of tulip plants is 1 mm wider than the average diameter of 4 randomly selected artificially supported stems of tulip plants?
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