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# Statistics: Considering Actual Production

You are trying to get an important new customer to buy a product that you produce. Their decision to buy depends on the speed at which you can produce the product once they have placed the order. Currently it takes you 70 hours on average to produce the product with a standard deviation of 8 hours. From historical data you have determined that actual production times follow a normal distribution.

Questions:
(a) What percent of the time can you produce the product within 80 hours?
(b) You want to promise that 95% of the time you will deliver the product in under __ hours?
(c) Assuming the standard deviation stays the same, how much do you have to reduce your average production time so that 95% of the time you can deliver the product in under 75 hours?

#### Solution Preview

mu = 70, sigma = 8; z = (x - mu)/sigma

a) mu = 70, sigma = 8; z = (x - mu)/sigma
P(x < 80 hours) = P(z < 1.25) = 0.8944
Therefore, 89.44% ...

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