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Helen [10]
3 years ago
14

Each day the wildlife commission releases 100 fish into the Durkee River in the following proportions: 55 brown trout and 45 rai

nbow trout.All of the fish swim through a watch station, one at a time,on the way upstream.which of the following expression represents the way to calculate the probability of a passing fish being a rainbow trout? 1. 45/55 2. 45/ 100 3. 55/100 4. 55-45/100 5. 45 +55 /100
Mathematics
1 answer:
bazaltina [42]3 years ago
6 0
45/100 so, 45 of every 100 fish should be rainbow trout.
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20 points Return to questionItem 4Item 4 20 points Police records in the town of Saratoga show that 13 percent of the drivers st
Sladkaya [172]

Answer:

a) 0.1423

b) 0.2977

c) 0.56

Step-by-step explanation:

For each driver stopped for speeding, there are only two possible outcomes. Either they have invalid licenses, or they do not. The probability of a driver having an invalid license is independent from other drivers. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem we have that:

13 percent of the drivers stopped for speeding have invalid licenses.

This means that p = 0.13

14 drivers are stopped

This means that n = 14

(a) None will have an invalid license.

This is P(X = 0)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{14,0}.(0.13)^{0}.(0.87)^{14} = 0.1423

(b) Exactly one will have an invalid license.

This is P(X = 1)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 1) = C_{14,1}.(0.13)^{1}.(0.87)^{13} = 0.2977

(c) At least 2 will have invalid licenses.

Either less than 2 have invalid licenses, or at least 2 does. The sum of the probabilities of these events is decimal 1. Mathematically, this is

P(X < 2) + P(X \geq 2) = 1

We want P(X \geq 2)

So

P(X \geq 2) = 1 - P(X < 2)

In which

P(X < 2) = P(X = 0) + P(X = 1) = 0.1423 + 0.2977 = 0.44

P(X \geq 2) = 1 - P(X < 2) = 1 - 0.44 = 0.56

8 0
3 years ago
Yesterday 5% of the 120 sixth graders at school were late. How many sixth graders were late?
attashe74 [19]

Answer:

6

Step-by-step explanation:

5% of 120 were late

= \frac{5}{100} × 120

= 0.05 × 120

= 6

6 0
3 years ago
Find y' if y=cos(x+5) multiple choice
Dmitry_Shevchenko [17]

Answer:

The last one is the correct answer.

Step-by-step explanation:


8 0
3 years ago
What is the sum of a 6-term geometric series if the first term is 21 and the last term is 1,240,029?
igor_vitrenko [27]
21 times x to the fifth (where x is the ratio between values) equals 1240029
1240029/21=59049
59049^(1/5)=9
so the values are 21, 21*9, 21*9^2, 21*9^3, 21*9^4, 1240029
the sum of these values is 1395030
5 0
3 years ago
Read 2 more answers
What is the image of point (4,3) if the rotation is -270
Gre4nikov [31]
Were is the image so i can help you

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3 years ago
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