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As part of a research project, the masses, m grams, of a random sample of 1000 pebbles from a certain beach were recorded. The results are summarised in the table. Mass (g) 50 < m < 150 150

As part of a research project, the masses, m grams, of a random sample of 1000 pebbles from a certain beach were recorded. The results are summarised in the table. Mass (g) 50 < m < 150 150

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter7: Applying Fractions
Section7.1: Ratios
Problem 21WE
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As part of a research project, the masses, m grams, of a random sample of 1000 pebbles from a certain beach were recorded. The results are summarised in the table. 150 <m < 200 200 < m < 250 250 <m < 350 318 Mass (g) 50 < m < 150 Frequency 162 355 165 (a) Calculate estimates of the mean and standard deviation of these masses. The masses, x grams, of a random sample of 1000 pebbles on a different beach were also found. It was proposed that the distribution of these masses should be modelled by the random variable X- N(200, 3600). (b) Use the model to find P(150 <X< 210). (c) Use the model to determine x, such that P(160 <X<x,) = 0.6. giving your answer correct to five significant figures. It was found that the smallest and largest masses of the pebbles in this second sample were 112g and 288 g respectively. (d) Use these results to show that the model may not be appropriate. (e) Suggest a different value of a parameter of the model in the light of these results.
Transcribed Image Text:As part of a research project, the masses, m grams, of a random sample of 1000 pebbles from a certain beach were recorded. The results are summarised in the table. 150 <m < 200 200 < m < 250 250 <m < 350 318 Mass (g) 50 < m < 150 Frequency 162 355 165 (a) Calculate estimates of the mean and standard deviation of these masses. The masses, x grams, of a random sample of 1000 pebbles on a different beach were also found. It was proposed that the distribution of these masses should be modelled by the random variable X- N(200, 3600). (b) Use the model to find P(150 <X< 210). (c) Use the model to determine x, such that P(160 <X<x,) = 0.6. giving your answer correct to five significant figures. It was found that the smallest and largest masses of the pebbles in this second sample were 112g and 288 g respectively. (d) Use these results to show that the model may not be appropriate. (e) Suggest a different value of a parameter of the model in the light of these results.
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