The length of life of an instrument produced by a machine has a normal distribution with a mean of 12 months and standard deviation of 2 months. Find the probability that an instrument produced by this machine will last a. less than 7 months. b. between 7 and 12 months.
Added by Raul H.
Step 1
This is done using the formula Z = (X - μ) / σ, where X is the value we're interested in, μ is the mean, and σ is the standard deviation. a. For less than 7 months, we calculate the Z score as follows: Z = (7 - 12) / 2 = -2.5. We then look up this Z score in a Show more…
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$\begin{array}{l}{\text { Machine Life }} \\ {\text { random variable with probability density function defined }} \\ {\text { by }}\end{array}$ $$f(t)=\frac{1}{11}\left(1+\frac{3}{\sqrt{t}}\right) \text { for } t \text { in }[4,9].$$ $\begin{array}{l}{\text { (a) Find the mean life of this machine. }} \\ {\text { (b) Find the standard deviation of the distribution. }} \\ {\text { (c) Find the probability that a particular machine of this }} \\ {\text { kind will last longer than the mean number of }} \\ {\text { years. }}\end{array}$
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