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A manufacturer knows that their items have a normally distributed length, with a mean of 19.3...

A manufacturer knows that their items have a normally distributed length, with a mean of 19.3 inches, and standard deviation of 3.8 inches.

If one item is chosen at random, what is the probability that it is less than 27.3 inches long?

Math   Statistics-And-Probability   
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Answer #1

Solution:

Given, X follows Normal distribution with,

   = 19.3

= 3.8

Find P(X < 27.3)

P(X < 27.3)

= P[(X - )/ <  (27.3 - )/]

= P[Z <  (27.3 - 19.3)/3.8]

= P[Z < 2.105]

= 0.9824 ... ( use z table)

Required probability =  0.9824

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