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Alona [7]
3 years ago
11

A bakery wants to determine how many trays of doughnuts it should prepare each day. Demand is normal with a mean of 5 trays and

standard deviation of 1 tray. If the owner wants a service level of at least 95%, how many trays should he prepare (rounded to the nearest whole tray)? Assume doughnuts have no salvage value after the day is complete. 6 5 4 7 unable to determine with the above information.
Mathematics
1 answer:
Alexeev081 [22]3 years ago
3 0

Answer:

4 trays should he prepared, if the owner wants a service level of at least 95%.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 5

Standard Deviation, σ = 1

We are given that the distribution of demand score is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

P(X > x) = 0.95

We have to find the value of x such that the probability is 0.95

P(X > x)  

P( X > x) = P( z > \displaystyle\frac{x - 5}{1})=0.95  

= 1 -P( z \leq \displaystyle\frac{x - 5}{1})=0.95  

=P( z \leq \displaystyle\frac{x - 5}{1})=0.05  

Calculation the value from standard normal z table, we have,  

\displaystyle\frac{x - 5}{1} = -1.645\\x = 3.355 \approx 4  

Hence,  4 trays should he prepared, if the owner wants a service level of at least 95%.

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k-4/3= 3

Mutiply both sides by 3 .

(3)(k-4/3)= (3)(3)

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2 years ago
Ieda and Thanh both offer piano lessons. Ieda charges an initial fee of $8.50 and an hourly rate of $11.00. Thanh charges an ini
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The price for each instructor will be the same at 3 hours. How I determined this answer:

First off, you need to add the initial price and hourly price for each person together, so you already know how much it will cost for 1 hour, including the initial fee. Here's how you do it:

Ieda: $11.00 (hourly price) + $8.50 (initial fee) = $19.50 (for 1 hour)

Thanh: $10.50 (hourly price) + $10.00 (initial fee) = $20.50 (for 1 hour)

Now that you have the price for 1 hour including the initial fee, now you need to find the price for each hour after that. Here's how I did that:

I created a graph that looked like this:

Hours:       1                 2                  3               
Ieda:      19.50          30.50         41.50
Thanh:   20.50          31.00         41.50

Here's how I figured out the price for each hour:

Ieda:

Hour 1 (including initial price):
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Hour 2 (excluding initial price): Only add the hourly price after Hour 1!
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Hour 3 (excluding initial price):
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Thanh:

Hour 1 (including initial price):
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Hour 2 (excluding initial price):
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Hour 3 (excluding initial price):
            $31.00 + $10.50 = $41.50

So, looking at the graph, their prices are the same once each instruction reaches 3 hours. ($41.50)

I hope I was able to help you! :)
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