Answer:
The probability that the laughter after one of the comedians jokes lasts for more than 7 seconds is approximately 0.474
Step-by-step explanation:
The nature of the distribution of the given data = Evenly distributed data
The range of the laughter times = Between 4 seconds and 9.7 seconds
The probability density function, f(x), is given as follows;
[tex]f(x) = \dfrac{1}{b - a}[/tex]
The mean of the uniform distribution, μ, is given as follows;
[tex]\mu = \dfrac{a + b}{2}[/tex]
The standard deviation, σ, is given as follows;
[tex]\sigma = \sqrt{\dfrac{\left (b - a\right)^2}{12} }[/tex]
Where;
a = 4, and b = 9.7, we have;
μ = (4 + 9.7)/2 = 6.85
σ = √((9.7 - 4)²/12) ≈ 1.64545
The probability density function, f(x) = 1/(b - a) for a ≤ x ≤ b
∴ f(x) = 1/(9.7 - 4)
For P(x > 7), we have;
P(x > 7) = 1 - P(x < 7) = 1 - (7 - 4) × 1/(9.7 - 4) ≈ 0.474
The probability that the laughter after one of the comedians jokes lasts for more than 7 seconds P(x >7) ≈ 0.474.
