Question

Managers at a local phone service wireless retail center have a goal that 70% of the center's customers will have to wait less than five minutes for service. The data below shows the wait times of a random sample of 25 customers in minutes. What is the probability of observing a sample proportion as low or lower than the data presented? Answer to three decimals: 0.123 for example.

4.1 | 5.4 | 2.6 | 9.8 | 3.5 |

3.8 | 0.4 | 7.8 | 4.2 | 5.8 |

4.2 | 2.6 | 3.5 | 9.9 | 6.2 |

1.5 | 0.8 | 9.2 | 3.2 | 5.9 |

2.5 | 5.3 | 3.2 | 2.3 | 4.5 |

Answer #1

Number of people who have to wait less than 5 minutes = 16

Proportion of people who have to wait less than 5 minutes, = 16/25 = 0.64

Population proportion, p = 0.70

n= 25

Probability of observing a sample proportion as low or lower than the data presented, P( < 0.64) =

So, the probability of observing a sample proportion as low or
lower than the data presented = **0.256**

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If you have any doubt ask me in comments.

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