The Sarasota Police department collected data on the number of car accidents ( X ) that occur each day on a certain stretch of route 41. From this data, they derived the probability distribution shown in the table below.
X P(X)
0 0.80
1 0.15
2 0.05
What is the expected mean (average) number of accidents that occur each day
To find the mean:
SUM [x * P(x)]
Multiply each x by its respective probability P(x). Add together for a total. This will be your mean.
To find variance:
SUM [x^2 * P(x)] - mean^2
Square each x. Multiply each squared x by its respective probability P(x). Add together for a total. Square the mean. Subtract the squared mean from the total. This will be your variance.
To find standard deviation:
Take the square root of the variance.
Hopefully, this information will help you with problems of this type.
1 to 6264. find the probability of selecting a number that is not divisible by 1000
To find the expected mean (average) number of accidents that occur each day, we need to multiply each possible number of accidents (X) by its corresponding probability (P(X)), and then sum up the results.
In this case, we have three possible numbers of accidents (X): 0, 1, and 2. We also have their corresponding probabilities: 0.80, 0.15, and 0.05.
So, to calculate the expected mean, we use the formula:
Expected Mean = (X1 * P(X1)) + (X2 * P(X2)) + (X3 * P(X3)) + ...
Let's calculate it step by step:
Expected Mean = (0 * 0.80) + (1 * 0.15) + (2 * 0.05)
Expected Mean = 0 + 0.15 + 0.10
Expected Mean = 0.25
Therefore, the expected mean (average) number of accidents that occur each day on this stretch of Route 41 is 0.25.