Jenny Soriano

Problem 8:

The following is the probability distribution of Jeanette’s study hours for Mathematics in a given week.

X (hours) | 2 | 4 | 5 | 6 |

P(X) | 0.21 | 0.39 | ? | .15 |

a) Find the probability of *X=5*.

b) Find the mean of the probability distribution.

c) Find the standard deviation of the probability distribution.

Answers

a) The easiest way to find the probability of X=5 is adding all the other X’s and subtracting 1 from the answer. The result of the subtraction is the probability of X=5

Steps:

0.21+0.39+.15= .75 → 1-.75= .25 → P(5)= .25

Reason: The probability distribution p(X) should always equals 1 when you add them up.

b) Find the mean of the probability distribution:

Steps: By making a probability distribution chart: ↓

x |
P(x) |
xp(x) |
x² p(x) |

2 |
0.21 |
.42 |
.84 |

4 |
0.39 |
1.56 |
6.24 |

5 |
0.25 |
1.25 |
6.25 |

6 |
0.15 |
.9 |
5.4 |

∑(x)= 7 |
∑p(x)= 1 |
∑xp(x)=4.13 |
∑ x²p(x)= 18.73 |

µ= mean/average

∑xp(x)= µ µ= 4.13 µ²= 17.0569

To find the standard deviation, you have to use the formula: ∑ x²p(x) – µ² ← has to be square rooted

the answer is…1.29