Joseph Mart recently purchased new trucks for its delivery fleet. The truck manufacturer confirmed
that the engines in the trucks have a mean failure time of 8 years, with a standard deviation of
1.5 years. Within what amount of time should Walmart expect for 93.32% of the trucks to fail?
Please show all work, with a normal distribution curve if possible, thanks in advance!
Solution:
Given: the trucks have a mean failure time of 8 years, with a standard deviation of 1.5 years.
That is : Mean = and standard
deviation =
We have to find the values of x such that:
P( x1 < X < x2 ) = 93.32%
P( x1 < X < x2 ) = 0.9332
Thus find z values such that:
P( -z < Z < z ) = 0.9332
If area between -z to +z is 0.9332 , then area outside this interval is = 1 - 0.9332 = 0.0668
That is area in tails is 0.0668
We divide this area in two tails equally
that is: 0.0668 / 2 = 0.0334 in left and right tail.
That is:
P( Z< -z) = 0.0334
and
P( Z> z )= 0.0334
Thus we get:
Thus from above graph we can see total area below z is:
P( Z< z ) = P( Z< -z ) + P( -z < Z < z )
P( Z< z ) = 0.0334 + 0.9332
P( Z< z ) = 0.9666
Thus look in z table for area = 0.9666 or its closest area and find z value.
Area 0.9664 is closest to 0.9666 and it corresponds to 1.8 and 0.03
thus z = 1.83
thus -z = -1.83
Now for finding x value we use formula:
and
Thus within 5.3 years to 10.7 years should Walmart expect for 93.32% of the trucks to fail.
Joseph Mart recently purchased new trucks for its delivery fleet. The truck manufacturer confirmed that the...
How can we assess whether a project is a success or a
failure?
This case presents two phases of a large business transformation project involving the implementation of an ERP system with the aim of creating an integrated company. The case illustrates some of the challenges associated with integration. It also presents the obstacles facing companies that undertake projects involving large information technology projects. Bombardier and Its Environment Joseph-Armand Bombardier was 15 years old when he built his first snowmobile...