GATE ME 2019 Set 1 — Question 14
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Engineering Mathematics → Statistics & Distributions → Normal Distribution
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Question
The lengths of a large stock of titanium rods follow a normal distribution with a mean () of and a standard deviation () of . What is the percentage of rods whose lengths lie between and ?
Correct answer
(A) 81.85\%
Solution
Given:
Mean () =
Standard deviation () = We need to find the percentage of rods with lengths between and , which is .First, convert the values to the standard normal variable using the formula:For :For :The required probability is :Using standard normal distribution tables:
Substituting these values:To find the percentage:Thus, the correct option is (A).
Mean () =
Standard deviation () = We need to find the percentage of rods with lengths between and , which is .First, convert the values to the standard normal variable using the formula:For :For :The required probability is :Using standard normal distribution tables:
Substituting these values:To find the percentage:Thus, the correct option is (A).
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