Respuesta :
Answer:
a) 2 accidents per day
b) .7071 accidents
Step-by-step explanation:
a) The mean is the sum of each possible number of accidents multiplied by its respective probability. So,
E(x) = (0)(.1) + (1)(.2) + (2)(.45) + (3)(.15) + (4)(.05) + (5)(.05) = 2
b) The variance V(x) = E(x^2) - E(x)^2, and the standard deviation is the square root of the variance. So,
V(x) = E(x^2) - (2)^2
= (0)(.1) + (1)(.2) + (4)(.45) + (9)(105) + (16)(.05) + (25)(.05) - 4 = 0.5
sqrt(0.5) = .7071
As per the probability distribution concept, there are 2 mean number of accidents per day in that city.
The standard deviation is 2.33.
What is probability distribution?
A probability distribution indicates the probability that a random variable can takes on certain values within a mentioned range.
The mean of any probability distribution can be calculated by multiplying the value of the data to the corresponding probability value.
Therefore, the mean probability distribution: μ = Σx * P(x).
Where, x is the value of the data and P(x) is the corresponding probability value.
Therefore, the mean number of accidents per day =
μ = (0 × 0.10) + (1 × 0.20) + (2 × 0.45) + (3 × 0.15) + (4 × 0.05) + (5 × 0.05)
= 2
The variance σ² = ∑[(x−μ)² P(x)]
Where, x is the random variable, μ is the mean probability distribution and P(x) is the corresponding probability value of x.
Therefore, σ² = ∑[(x−μ)² P(x)]
= (0 - 2)² × 0.10 + (1 - 2)² × 0.20 + (2 - 2)² × 0.45 + (3-2)² × 0.15 + (4-2)² × 0.05 + (5 - 2)² × 0.5
= 0.4 + 0.2 + 0 + 0.15 + 0.2 + 4.5
= 5.45
Therefore, standard deviation = σ = √(σ²) = √5.45 = 2.33
a) There are 2 mean number of accidents per day.
b) The standard deviation is 2.33.
Learn more about probability distribution here: https://brainly.com/question/15930185
#SPJ2
