Question

In: Statistics and Probability

The average tensile strength for a particular aircraft bolt is 32.06 kN with a variance of...

The average tensile strength for a particular aircraft bolt is 32.06 kN with a variance of 0.01 kN. What proportion of bolts will have a tensile strength less than 31.9 and more than 32.3 kN?

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Expert Solution

Define random variable X be the tensile strength for a particular aircraft bolt.

Assume that the X has normal distribution with mean and standard deviation are,

Average tensile strength for particular aircraft bolt =

Variance =

Standard deviation =

Here we have to find P(31.9 < X < 32.3)

                                          

                                          = P(-1.6 < z < 2.4)                   where z is standard normal variable

                                          = P(z < 2.4) - P(z < -1.6)

                                          = 0.9918 - 0.0548             (From statistical table of z values)

                                         = 0.937

Proportion of bolts having a tensile strength less than 31.9 and more than 32.3 kN is 0.937

orchestra answered 2 years ago
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