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Blababa [14]
3 years ago
9

Suppose that 80 percent of all statisticians are shy, whereas only 15 percent of all economists are shy. Suppose also that 90 pe

rcent of the people at a large gathering are economists and the other 10 percent are statisticians. If you meet a shy person at random at the gathering. What is the probability that the person is a statistician?
Mathematics
1 answer:
Anna71 [15]3 years ago
3 0

Answer:

37.21% probability that the person is a statistician.

Step-by-step explanation:

We have these following probabilities:

An 80% probability that a statistican is shy.

A 15% probability that an economist is shy.

At the gathering, a 90% probability that a person is an economist.

At the gathering, a 10% probability that a person is a statistican.

If you meet a shy person at random at the gathering. What is the probability that the person is a statistician?

This can be formulated as the following question:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

P = \frac{P(B).P(A/B)}{P(A)}

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

So

What is the probability that the person is a statistican, given that he is shy?

P(B) is the probability of the person being a statistican. So P(B) = 0.1.

P(A/B) is the probability of a statistican being shy, so P(A/B) = 0.8.

P(A) is the probability of a person being a shy. This is 15% of 90%(economists) and 80% of 10%(statisticans). So

P(A) = 0.15*0.9 + 0.8*0.1 = 0.215

Finally

P = \frac{P(B).P(A/B)}{P(A)}

P = \frac{0.1*0.8}{0.215} = 0.3721

37.21% probability that the person is a statistician.

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Avery can run at 10 uph. The bank of a river is represented by the line 4x + 3y = 12, and Avery is at (7, 5). How much time does
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The minimum distance will be along a perpendicular line to the river that passes through the point (7,5)

4x+3y=12

3y=-4x+12

y=-4x/3+12/3

So a line perpendicular to the bank will be:

y=3x/4+b, and we need it to pass through (7,5) so

5=3(7)/4+b

5=21/4+b

20/4-21/4=b

-1/4=b so the perpendicular line is:

y=3x/4-1/4

So now we want to know the point where this perpendicular line meets with the river bank.  When it does y=y so we can say:

(3x-1)/4=(-4x+12)/3  cross multiply

3(3x-1)=4(-4x+12)

9x-3=-16x+48

25x=51

x=51/25

x=2.04

y=(3x-1)/4

y=(3*2.04-1)/4

y=1.28

So now that we know the point on the river that is closest to Avery we can calculate his distance from that point...

d^2=(x2-x1)^2+(y2-y1)^2

d^2=(7-2.04)^2+(5-1.28)^2

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Since he can run at 10 uph...

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So it will take him 0.62 hours or 37 minutes and 12 seconds for him to reach the river.




8 0
3 years ago
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Answer:

Lowest score needed=4.92

Step-by-step explanation:

Using the standard normal distribution table we find the value of standard normal deviate corresponding to area of 15%

For area of 15% we have Z= -1.04

Thus we have

Z=\frac{X-\overline{X}}{\sigma }\\\\\therefore X=\sigma Z+\overline{X}\\\\

Applying values we get

X=-1.04\times 2+7\\\\X=4.92

Thus lowest score needed = 4.92

3 0
3 years ago
Graph: y – 3 = } (x + 2)
Natalija [7]

Answer:x2 355b.  Hhgguyuy

Step-by-step explanation:

7 0
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