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(b) A company produces cylindrical metal rods. The diameters of rods have a normal distribution with mean µcm and variance o² cm². A random sample of 100 rods is taken and the diameter x, in cm, of each rod is measured. The results are summarised as Ex=52.1 and r=27.303. Calculate the mean and variance of the population of the diameters of the rods (iii) Detemine a 95% confidence interval for the mean diameter of the rods. (iv) Investigate, at the 1% significance level, whether the mean diameter of the rods is 0.512 cm.

(b) A company produces cylindrical metal rods. The diameters of rods have a normal distribution with mean µcm and variance o² cm². A random sample of 100 rods is taken and the diameter x, in cm, of each rod is measured. The results are summarised as Ex=52.1 and r=27.303. Calculate the mean and variance of the population of the diameters of the rods (iii) Detemine a 95% confidence interval for the mean diameter of the rods. (iv) Investigate, at the 1% significance level, whether the mean diameter of the rods is 0.512 cm.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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(b) A company produces cylindrical metal rods. The diameters of rods have a normal distribution with mean ucm and variance o' cm?. A random sample of 100 rods is taken and the diameter x, in cm, of each rod is measured. The results are summarised as Ex=52.1 and x = 27.303. (1) Calculate the mean and variance of the population of the diameters of the rods (iii) Detemine a 95% confidence interval for the mean diameter of the rods. (iv) Investigate, at the 1% significance level, whether the mean diameter of the rods is 0.512 cm.
Transcribed Image Text:(b) A company produces cylindrical metal rods. The diameters of rods have a normal distribution with mean ucm and variance o' cm?. A random sample of 100 rods is taken and the diameter x, in cm, of each rod is measured. The results are summarised as Ex=52.1 and x = 27.303. (1) Calculate the mean and variance of the population of the diameters of the rods (iii) Detemine a 95% confidence interval for the mean diameter of the rods. (iv) Investigate, at the 1% significance level, whether the mean diameter of the rods is 0.512 cm.
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