The county highway department recorded the following probabilities for the number ol ac a certain freeway for one month. The number of accidents per day and their corresponding probabilities are shown. (Round your answers to three decimal places if needed.) Number of accidents, X 0 1 2 3 4 Probability P(X) 0.3 0.2 y 0.2 |0.1 a. Find y so that this is a valid probability distribution. b. Find the mean of this distribution using the value found for y in part a. c. Find the expected value of number of accidents per day. d. The variance and standard deviation of this distribution using the value found for y in part a are respectively, and

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The county highway department recorded the following probabilities for the number of accidents per day on a certain freeway for one month. The number of accidents per day and their corresponding probabilities are shown. (Round your answers to three decimal places if needed.)

| Number of accidents, X | 0   | 1   | 2  | 3   | 4   |
|------------------------|-----|-----|----|-----|-----|
| Probability P(X)       | 0.3 | 0.2 | y  | 0.2 | 0.1 |

a. Find y so that this is a valid probability distribution.

b. Find the mean of this distribution using the value found for y in part a.

c. Find the expected value of the number of accidents per day.

d. The variance and standard deviation of this distribution using the value found for y in part a are respectively, ______ and ______.
Transcribed Image Text:The county highway department recorded the following probabilities for the number of accidents per day on a certain freeway for one month. The number of accidents per day and their corresponding probabilities are shown. (Round your answers to three decimal places if needed.) | Number of accidents, X | 0 | 1 | 2 | 3 | 4 | |------------------------|-----|-----|----|-----|-----| | Probability P(X) | 0.3 | 0.2 | y | 0.2 | 0.1 | a. Find y so that this is a valid probability distribution. b. Find the mean of this distribution using the value found for y in part a. c. Find the expected value of the number of accidents per day. d. The variance and standard deviation of this distribution using the value found for y in part a are respectively, ______ and ______.
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