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tangare [24]
2 years ago
5

Your mother asked you to turn the oven down to 325°F. This is 75°F less than it was. What was the original temperature?

Mathematics
2 answers:
navik [9.2K]2 years ago
5 0
The original was 400f
325+75=400
DanielleElmas [232]2 years ago
4 0
The original was 400 F
325 + 75= 400
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A machine is used to fill Apple Juice bottles with juice. The machine has a known standard deviation of σ = 0.05 liters. The tar
Lina20 [59]

Answer:

The probability that the quality control manager will shut down the machine is 0.0002.

Step-by-step explanation:

We are given that a machine is used to fill Apple Juice bottles with juice. The machine has a known standard deviation of σ = 0.05 liters. The target mean fill volume is µ = 2.0 liters.

A quality control manager obtains a random sample of 50 bottles. He will shut down the machine if the sample of these 50 bottles is less than 1.95 or greater than 2.1.

<u><em>Let </em></u>\bar X<u><em> = sample mean fill volume</em></u>

The z score probability distribution for sample mean is given by;

                               Z  = \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \mu = population mean fill volume = 2 liters

           \sigma = standard deviation = 0.05 liters

           n = sample of bottles = 50

Now, it is provided that he will shut down the machine if the sample of these 50 bottles is less than 1.95 or greater than 2.1.

  • So, Probability that the sample of these 50 bottles is less than 1.95 is given by = P(\bar X < 1.95)

         P(\bar X < 1.95) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < \frac{1.95-2}{\frac{0.05}{\sqrt{50} } } ) = P(Z < -7.07) = 1 - P(Z \leq 7.07)

                                                         = 1 - 0.9999 = 0.0001

  • Probability that the sample of these 50 bottles is greater than 2.1 is given by = P(\bar X > 2.1)

        P(\bar X > 2.1) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } > \frac{2.1-2}{\frac{0.05}{\sqrt{50} } } ) = P(Z > 14.14) = 1 - P(Z < 14.14)

                                                     = 1 - 0.9999 = 0.0001

Because the highest critical value in the z table is given as x = 4.40 for area of 0.99999.

Therefore, probability that the quality control manager will shut down the machine = 2 \times 0.0001 = 0.0002.

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