Question

The following chart represents the probability distribution for the numbers of employees absent per day at a medium-sized business.

x( # of the employees absent) | f(x) probability |

0 | 0.3 |

1 | 0.2 |

2 | 0.1 |

3 | 0.3 |

4 | 0.1 |

1. What is the probability that at least 4 employees will be absent?

2. What is the probability that 1 or more employees will be absent?

3. What is the probability that fewer than 3 employees will be absent?

4. What is the expected value for the number of employees absent?

5. What is the variance for the number of employees absent?

6. What is the standard deviation for the number of employees absent?

Answer #1

Solution :

(a)

P(X 4) = 0.1

Probability = 0.1

(b)

P(X 1) = 0.2 + 0.1 + 0.3 + 0.1 = 0.7

Probability = 0.3

(c)

P(x < 3) = 0.3 + 0.2 + 0.1 = 0.6

Probability = 0.6

(d)

Mean = = X * P(X)

= 0 * 0.3 + 1 * 0.2 + 2 * 0.1 + 3 * 0.3 + 4 * 0.1

= 0 + 0.2 + 0.2 + 0.9 + 0.4

= 1.7

variance =

=
X ^{2} * P(X) -
^{2}

= 0 * 0.3 + 1^{2} * 0.2 + 2^{2} * 0.1 +
3^{2} * 0.3 + 4^{2} * 0.1 - 1.7^{2}

variance = 2.01

(e)

Standard deviation = 2.01 = 1.4177

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