A certain machine produces components having a mean length of 15 cm. As a result of measuring samples of these components, it is found that the standard deviation is 0.2 cm. A test is carried out on a sample to check whether the data on the lengths of the components is normally distributed and it is found that this is so, determine the number of components likely to have a length of less than 14.95 cm in a batch of 1000 components.

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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A certain machine produces components having a mean length of 15 cm. As a result of measuring samples of these components, it is found that the standard deviation is 0.2 cm. A test is carried out on a sample to check whether the data on the lengths of the components is normally distributed and it is found that this is so, determine the number of components likely to have a length of less than 14.95 cm in a batch of 1000 components.

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