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3 years ago

Help? It’s on probability’s.

Mathematics

2 answers:

yan [13]3 years ago

5 0

Answer:

1. A' (A prime) is everything that is NOT in A, so it would be anything not in the circle for A (including the intercepts). This means the answer to 1 is 4,6,8,2,and 10.

2. B', so anything that is not in B - 1,7 and 2

3. AnB (A intersect B) this is anything that is in BOTH a AND b, so everything in the middle section or the section between A and B. this would be just 3.

4. AUB (A union B) this is EVERYTHING in both A and B - so everything in the A and B circles - 1,7,3,10,4,6, and 8.

5. A' UB (A prime union B) - this is everything that is NOT in A and B (basically everything in C thats not in A and everything in B thats not in A) - 4,6 and 8.

6. An(BUC) (A intersect of B union C) this is everything that is both in A and B and C. (remember it MUST also be in A) - 3 and 7 only is the answer

7. AU (BnC) - this is A plus everything that is in the section between B and C (so basically any number that is in all three sets) - nothing fits these criteria as there is nothing in the center section.

8. An(BUC') this one is a little harder to understand. C' is everything that is NOT in the C circle, so EVERYTHING in A and EVERYTHING in B. The intercept of An (BUC') would be 1 and 3 since A is included in C prime.

Im sorry I dont explain these well but basically understand these things:

If a letter has a ' after it ( for example A'), it means everything EXCEPT what is in that set.

the U means UNION. An easy way to remember what to do is that in a Union things come together, so for example if you are asked AUB, you should list EVERYTHING in both set A and set B.

n means INTERSECTION. An easy way to remember this is that an intersection (like on the road) is when two things cross paths. When you are asked AnB, you are being asked any number that is in BOTH A and B.

deff fn [24]3 years ago

3 0

B it’s prob a move but ya

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3 years ago

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 = dosage of the active ingredient

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 = 0.0013

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)

= 0.00001

6 0

3 years ago

NEED HELP NOW!!

irinina [24]

Answer:

i am not sure to my answer

my answer is letter D

8 0

3 years ago

Read 2 more answers