# Find the probability that in 200 tosses of a fair die, we will obtain at least 40 fives

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Find the probability that in 200 tosses of a fair die, we will obtain at least 40 fives

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Step 1

Binomial approximation:

The normal distribution can be used as an approximation to the binomial distribution, under certain circumstances, namely:

• If X ~ B (n, p) and if n is large and/or p is close to ½, then X is approximately N (np, npq)

(where q = 1 - p).

Continuity Correction:

The binomial and Poisson distributions are discrete random variables, whereas the normal distribution is continuous. We need to take this into account when we are using the normal distribution to approximate a binomial or Poisson using a continuity correction.

Continuity correction factor table:

If   P(X=n) use   P(n – 0.5 < X < n + 0.5)
If   P(X > n) use   P(X > n + 0.5)
If   P(X ≤ n) use    P(X < n + 0.5)
If    P (X < n) use   P(X < n – 0.5)
If    P(X ≥ n) use   P(X > n – 0.5)

z-score:

If a random variable X has a distribution with mean µ and standard deviation σ, then the z-score is defined as,

Step 2

Computing the probability that at least 26 people experience flu symptoms:

Let the random variable X represents the number of fives obtained.

The probability getting a 5 when a die is tossed is 1/6.

The die is tossed 200 times.

That is, the random variable X follows binomial dis... help_outlineImage TranscriptioncloseMean = np 1 =200 6 - 33.33 Standard devaition = o -Vnp (1- p) 5 1 200 6 1 6 - 5.27 fullscreen

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