Question

A student takes a multiple choice test consisting of 5 questions where there are 4 choices per question. Also, each question is worth 20 points. Suppose the student guesses on each question. Let X be the number of questions the student gets correct. The probability distribution for X is given below. Find the variance of X. Do not give units and give your answer to four decimal places.

x | 0 | 1 | 2 | 3 | 4 | 5 |

P(X=x) | 0.2373 | 0.3955 | 0.2637 | 0.0879 | 0.0146 | .0010 |

Answer #1

Solution:

The formula for variance is given as below:

Variance = ∑ P(X)*(X - mean)^2

The calculation table is given as below:

X |
P(X) |
XP(X) |
(X - mean)^2 |
P(X)*(X - mean)^2 |

0 |
0.2373 |
0 |
1.5625 |
0.37078125 |

1 |
0.3955 |
0.3955 |
0.0625 |
0.02471875 |

2 |
0.2637 |
0.5274 |
0.5625 |
0.14833125 |

3 |
0.0879 |
0.2637 |
3.0625 |
0.26919375 |

4 |
0.0146 |
0.0584 |
7.5625 |
0.1104125 |

5 |
0.001 |
0.005 |
14.0625 |
0.0140625 |

Total |
1 |
1.25 |
0.9375 |

Variance = ∑ P(X)*(X - mean)^2

Variance = 0.9375

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