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Sindrei [870]
3 years ago
12

You consider yourself a bit of an expert at playing rock-paper-scissors and estimate that the probability that you win any given

game is 0.5. In a tournament that consists of playing 60 games of rock-paper-scissors let X be the random variable that is the of number games won. Assume that the probability of winning a game is independent of the results of previous games. You should use the normal approximation to the binomial to calculate the following probabilities. Give your answers as decimals to 4 decimal places. a)Find the probability that you win at least 35 of the games. P(X ≥ 35) =b)Find the probability that you win less than 27 games. P(X < 27) =c)Find the probability that you win between 30 and 40 games. P(30 ≤ X ≤ 40) =
Mathematics
1 answer:
cestrela7 [59]3 years ago
7 0

Answer:

a) 0.37

b) 0.421

c) 0.25

Step-by-step explanation:

Since the probability of winning a game is binomial (P = 0.5) the expected value for number of winning when you play 60 games is

\mu = 60*0.5 = 30

And the standard deviation:

\sigma = 60*0.5*0.5 = 15

a) the cumulative probability of winning at least 35 games is

P(X \geq 35) = 1 - P(X < 35) = 1 - 0.631 = 0.37

b)P(X < 27) = 0.421

c)P(30 \leq X \leq 40) = P(X \leq 40) - P(X \leq 30) = 0.75 - 0.5 = 0.25

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harina [27]

Answer:

  • f(n) = n^2 +1
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Step-by-step explanation:

The first differences of the sequence are ...

  • 5-2 = 3
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Second differences are ...

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The second differences are constant, so the sequence can be described by a second-degree polynomial.

We can write and solve three equations for the coefficients of the polynomial. Let's define the polynomial for the sequence as ...

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Then the first three terms of the sequence are ...

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Subtracting the first equation from the other two gives ...

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Subtracting the first of these from half the second gives ...

  (4a +b) -(3a +b) = (4) -(3)

  a = 1 . . . . . simplify

Substituting into the first of the 2-term equations, we get ...

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And substituting the values for a and b into the equation for f(1), we have ...

  1·1 + 0 + c = 2

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So, the formula for the sequence is ...

  f(n) = n^2 + 1

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The 20th term is f(20):

  f(20) = 20^2 +1 = 401

_____

<em>Comment on the solution</em>

It looks like this matches the solution of the "worked example" on your problem page.

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