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Natali5045456 [20]
2 years ago
11

Mary won £5000 in a competition

Mathematics
1 answer:
Ahat [919]2 years ago
5 0

Answer: £833

Step-by-step explanation:

1. Multiply 279 by 9 (equals 2,511)

2. Multiply 184 by 9 (1,656)

3. Add 2,511 and 1,656 together (4,167)

4. Subtract 4,167 from 5,000 (833)

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Which of the following statement must be true?I WILL MARK THE BRAINIEST
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d) XY > RS

Step-by-step explanation:

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A recent report indicated that 22 percent of the households in a certain community speak a
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2 years ago
23% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and as
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Answer:

a) There is a 29.42% probability that the number of college students who say they use credit cards because of the rewards program is exactly two.

b) There is a 41.37% probability that the number of college students who say they use credit cards because of the rewards program is more than two.

c) There is a 69.49% probability that the number of college students who say they use credit cards because of the rewards program is between two and five, inclusive.

Step-by-step explanation:

There are only two possible outcomes. Either the student use credit cards because of the rewards program, or they use for other reason. So, we can solve this exercise using the binomial probability distribution.

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}.\pi^{x}.(1-\pi)^{n-x}

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

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

And \pi is the probability of X happening.

In this problem, we have that:

10 students are randomly selected, so n = 10.

23% of college students say they use credit cards because of the rewards program. This means that \pi = 0.23

(a) exactly two

This is P(X = 2).

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

P(X = 2) = C_{10,2}.(0.23)^{2}.(0.77)^{8} = 0.2942

There is a 29.42% probability that the number of college students who say they use credit cards because of the rewards program is exactly two.

(b) more than​ two

This is P(X > 2).

Either a value is larger than two, or it is smaller of equal. The sum of the decimal probabilities of these events must be 1. So:

P(X \leq 2) + P(X > 2) = 1

P(X > 2) = 1 - P(X \leq 2)

In which

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)

So

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

P(X = 0) = C_{10,0}.(0.23)^{0}.(0.77)^{10} = 0.0733

P(X = 1) = C_{10,1}.(0.23)^{1}.(0.77)^{9} = 0.2188

P(X = 2) = C_{10,2}.(0.23)^{2}.(0.77)^{8} = 0.2942

P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0733 + 0.2188 + 0.2942 = 0.5863

P(X > 2) = 1 - P(X \leq 2) = 1 - 0.5863 = 0.4137

There is a 41.37% probability that the number of college students who say they use credit cards because of the rewards program is more than two.

(c) between two and five inclusive.

This is

P = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

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

P(X = 2) = C_{10,2}.(0.23)^{2}.(0.77)^{8} = 0.2942

P(X = 3) = C_{10,3}.(0.23)^{3}.(0.77)^{7} = 0.2343

P(X = 4) = C_{10,4}.(0.23)^{4}.(0.77)^{6} = 0.1225

P(X = 5) = C_{10,3}.(0.23)^{5}.(0.77)^{5} = 0.0439

So

P = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.2942 + 0.2343 + 0.1225 + 0.0439 = 0.6949

There is a 69.49% probability that the number of college students who say they use credit cards because of the rewards program is between two and five, inclusive.

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