A car insurance company has determined that 7% of all drivers were involved in a car accident last year. The company randomly selects 200 drivers. Compute the mean and standard devistion of the random variable, x, the number of drivers involved in accidents last year.
Well, if 7% of all drivers were involved in an accident last year, then we can say that the probability of any given driver being involved in an accident is 0.07.
Now, since the company randomly selects 200 drivers, we can treat this as a binomial distribution problem. The mean (μ) of a binomial distribution is given by the formula: μ = n * p, where n is the number of trials (in this case, 200) and p is the probability of success (0.07).
So, μ = 200 * 0.07 = 14.
For the standard deviation (σ) of a binomial distribution, the formula is: σ = sqrt(n * p * (1 - p)).
Plugging in the values, we get σ = sqrt(200 * 0.07 * (1 - 0.07)).
Now, let me just grab my calculator... *rummages through pockets*
Ah, here it is! *dusts off calculator*
Calculating... *taps calculator buttons*
σ ≈ 3.662... *drum roll*
So, the mean (μ) is approximately 14, and the standard deviation (σ) is approximately 3.662.
To compute the mean and standard deviation of the random variable x, the number of drivers involved in accidents last year, we can use the properties of a binomial distribution.
Given that the car insurance company has determined that 7% of all drivers were involved in a car accident last year, this can be considered as a binomial distribution with the following parameters:
- Probability of success (p): 0.07 (7%)
- Number of trials (n): 200
Mean (μ) = np
= 200 * 0.07
= 14
Standard Deviation (σ) = √(np(1-p))
= √(200 * 0.07 * (1 - 0.07))
= √(200 * 0.07 * 0.93)
≈ √13.86
≈ 3.72
Therefore, the mean (μ) of the random variable x is 14, and the standard deviation (σ) is approximately 3.72.
To compute the mean and standard deviation of the random variable x, we need to use the concept of a binomial distribution.
The mean of a binomial distribution is given by the formula:
μ = n * p
where μ represents the mean, n represents the number of trials, and p represents the probability of success.
In this case, the number of trials is 200 (as the company randomly selects 200 drivers), and the probability of success (drivers being involved in a car accident) is 0.07 (since 7% of all drivers were involved in a car accident last year).
So, μ = 200 * 0.07 = 14.
Therefore, the mean number of drivers involved in accidents last year is 14.
Now, let's calculate the standard deviation:
The standard deviation of a binomial distribution is given by the formula:
σ = sqrt(n * p * q)
where σ represents the standard deviation, n represents the number of trials, p represents the probability of success, and q represents the probability of failure (which is equal to 1 - p).
In this case, the number of trials is 200, the probability of success is 0.07, and the probability of failure is 1 - 0.07 = 0.93.
So, σ = sqrt(200 * 0.07 * 0.93) ≈ 4.47.
Therefore, the standard deviation of the random variable x is approximately 4.47.