C) Workout using factorization. Show all your working. 9.9²- 0.1²
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The probability that it rains at most 2 days is 0.00005995233 and the variance is 0.516
<h3>The probability that it rains at most 2 days</h3>The given parameters are:
- Number of days, n = 7
- Probability that it rains, p = 95%
- Number of days it rains, x = 2 (at most)
The probability that it rains at most 2 days is represented as:
P(x ≤ 2) = P(0) + P(1) + P(2)
Each probability is calculated as:
So, we have:
So, we have:
P(x ≤ 2) =0.00000002097 + 0.00000168821 + 0.00005824315
P(x ≤ 2) = 0.00005995233
Hence, the probability that it rains at most 2 days is 0.00005995233
<h3>The mean</h3>This is calculated as:
Mean = np
So, we have:
Mean = 7 * 92%
Evaluate
Mean = 6.44
Hence, the mean is 6.44
<h3>The standard deviation</h3>This is calculated as:
σ = √np(1 - p)
So, we have:
σ = √7 * 92%(1 - 92%)
Evaluate
σ = 0.718
Hence, the standard deviation is 0.718
<h3>The variance</h3>We have:
σ = 0.718
Square both sides
σ² = 0.718²
Evaluate
σ² = 0.516
This represents the variance
Hence, the variance is 0.516
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