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Elenna [48]
3 years ago
11

What's the correct formula for this function? ​

Mathematics
2 answers:
Reptile [31]3 years ago
8 0

Answer:

Option C. y = -2x + 3

Step-by-step explanation:

When we look at this function we see that it has a negative slope and the y-intercept is equal to (0,3).  From this we know that the function we are looking for will be looking like...

y = mx + 3

And as I said earlier since the slope is negative, the only right option is this case will be Option C

RUDIKE [14]3 years ago
5 0

Answer:

The correct anwer is (C) : y = - 2x + 3

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Suppose a certain capsule is manufactured so that the dosage of the active ingredient follows the distribution Y ~ N(μ = 10 mg,
lianna [129]

Answer:

(a) Probability that Y falls into the dangerous region is 0.0013.

(b) Probability that the mean Y-bar falls into the dangerous region is 0.00001.

Step-by-step explanation:

We are given that a certain capsule is manufactured so that the dosage of the active ingredient follows the distribution Y ~ N(μ = 10 mg, σ = 1 mg).

A dosage of 13 mg is considered dangerous.

Let Y = <u><em>dosage of the active ingredient </em></u>

The z-score probability distribution for normal distribution is given by;

                                 Z  =  \frac{ Y-\mu}{\sigma} } }  ~ N(0,1)

where, \mu = population mean = 10 mg

            \sigma = standard deviation = 1 mg

(a) Probability that Y falls into the dangerous region is given by = P(Y \geq 13 mg)

       P(Y \geq 13 mg) = P( \frac{ Y-\mu}{\sigma} } } \geq \frac{ 13-10}{1} } } ) = P(Z \geq 3) = 1 - P(Z < 3)  

                                                          = 1 - 0.9987 = <u>0.0013</u>

The above probability is calculated by looking at the value of x = 3 in the z table which has an area of 0.9987.

(b) We are given that a dosage of 13 mg is considered dangerous. And we sample 49 capsules at random.

Let \bar Y = sample mean dosage

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

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

where, \mu = population mean = 10 mg

            \sigma = standard deviation = 1 mg

            n = sample of capsules = 49

So, Probability that the mean Y-bar falls into the dangerous region is given by = P(\bar Y \geq 13 mg)

          P(Y \geq 13 mg) = P( \frac{\bar Y-\mu}{\frac{\sigma}{\sqrt{n} } } } } \geq \frac{13-10}{\frac{1}{\sqrt{49} } } } } ) = P(Z \geq 21) = 1 - P(Z < 21)  

                                                             = <u>0.00001</u>

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