# STATISTICS CHAPTER 5

Sec5.1

- A standard deck of playing cards has 52 cards. There are four suits-spades, hearts, diamonds, and clubs – with 13 cards in each suit. Spades and clubs are black; hearts and diamonds are red. If one of these cards is selected at random, what is the probability that it is
- six?
- black?
- not a diamond?

- The following table provides a frequency distribution for the number of rooms in this county’s housing units. The frequencies are in thousands. A housing unit is selected at random.

Rooms | No. of units |

1 | 10 |

2 | 11 |

3 | 54 |

4 | 32 |

5 | 45 |

6 | 24 |

7 | 47 |

8+ | 17 |

- Find the probability that the housing unit obtained has four rooms. The probability is _____________
- Find the probability that the housing unit obtained has more than four rooms. The probability is ____________
- Find the probability that the housing unit obtained has one or two rooms. The probability is ____________
- Find the probability that the housing unit obtained has fewer than one room. The probability is __________
- Find the probability that the housing unit obtained has one or more rooms. The probability is _____________

- When two balanced dice are rolled, complete part A through D below.
- Determine the probability that the sum of the dice is 9. _________
- Determine the probability that the sum of the dice is odd. ________
- Determine the probability that the sum of the dice is 5 or 10. ________
- Determine the probability that the sum of the dice is 12, 4, or 11. _________

- A balanced dime is tossed three times. The possible outcomes are represented in the below. Complete part (a) through (d) below.

HHH HTH THH TTH HHT HTT THT TTT

- Find the probability that all three of the tosses come up heads. _____
- Find the probability that the last two tosses come up tails. ______
- Find the probability that all three tosses come up the same. _____
- Find the probability that the third toss comes up tails. ______

Sec.5.2 & sec.5.3

- When one die is rolled, the following six outcomes are possible. List the outcomes constituting

A = event the die comes up odd, B = event the die comes up 5 or more

C = event the die comes up at most 3, D = event the die comes up 6

What outcomes constitute event A?

What outcomes constitute event B?

What outcomes constitute event C?

What outcomes constitute event D?

What outcomes constitute event (not A)?

What outcomes constitute event (B or C)?

What outcomes constitute event (A and D)?

- The age distribution for politicians in a certain country is shown in the accompanying table. Suppose that a politician is selected at random. Let events A, B, C, and S be defined as follows.

A = event the politician is under 50

B = event the politician is in his or her 50s

C = event the politician is in his or her 60s

S = event the politician is under 70

Age(yr) | No. of politicians |

Under 50 | 11 |

50-59 | 35 |

60-69 | 33 |

70-79 | 21 |

80 and over | 4 |

- Use the table and the f/N rule to find P(S)
- Express event S in terms of events A, B, and C.
- Determine P(A), P(B), and P(C)
- Compute P(S), using the special addition rule and your answers from parts B and C. Compare your answer with that in part A.

- A recent census found that 51.6% of adults are female, 10.1% are divorced, and 5.9% are divorced females. For an adult selected at random, let F be the event that the person is female, and D be the event that the person is divorced.
- Obtain P(F), P(D), and P(F and D)
- Determine P(F or D)
- Find the probability that a randomly selected adult is male.

Sec.5.4

- A variable y of a finite population has the frequency distribution shown in the table. Suppose a member is selected at random from the population and let Y denote the value of the variable y for the member obtained.

Y | 4 | 5 | 6 | 7 |

f | 2 | 2 | 9 | 7 |

- Determine the probability distribution of the random variable Y.

Y | 4 | 5 | 6 | 7 |

P(Y=y) |

- Use random-variable notation to describe the events that Y takes on the value 6, a value less than 6, and a value of at least 6.

The event that Y takes on the value 6 can be represented as { }

The event that Y takes on a value less than 6 can be represented as { }

The event that Y takes on a value of at least 6 can be represented as { }

- Find P(Y=6), P(Y<6), and P(Y6).

- Construct a probability histogram for the random variable Y.

- Suppose T and Z are random variables.
- If P(T>2.26) = 0.03 and P(T<-2.26)=0.03, obtain P(-2.26 T26)

- If P(-2.05 Z 05) = 0.96 and also P(Z>2.05)=P(Z<-2.05). Find P(Z>2.05)

Sec. 5.5

- The table below shows the probability distribution of the random variable X.

X | 1 | 2 | 3 |

P(X=x) | 0.3 | 0.2 | 0.5 |

- Find the mean of the random variable.

- Obtain the standard deviation of the random variable.

- A factory manager collected data on the number of equipment breakdowns per day. From those data, she derived the probability distribution shown to the table, where W denotes the number of breakdowns on a given day.

W | 0 | 1 | 2 |

P(W=w) | 0.80 | 0.15 | 0.05 |

- Determine (Round to three decimal places as needed)
- On average, how many breakdowns occur per day?
- About how many breakdowns are expected during a 1-year period, assuming 250 work days per year?
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