Question 1 [9]

A college placement office sent a questionnaire to a sample of business school graduates requesting information on monthly starting salaries. Below are the monthly starting salaries for the sample of 12 business school graduates (in dollars):

3850 | 3950 | 4050 | 3880 | 3755 | 3710 |

3890 | 4130 | 3940 | 4325 | 3920 | 3880 |

a) Calculate the mean, median and mode monthly starting salary for this sample of business school graduates. Interpret your results (rounded off to two decimals where possible). [4]

b) Comment on the skewness of the distribution using the values calculated in a). [1]

c) Calculate the variance (rounded off to two decimals). [2]

d) Calculate and interpret the 86th percentile (rounded off to zero decimals). [2]

Bonus Question: Use Excel and the Data Analysis Add-on to create a descriptive summary of the data above. [3]

Question 2 [6]

The liquid detergent cartons of a particular brand are automatically filled on a production line. The filling weights has a bell-shaped distribution. It is found that the mean filling weight is 470 millilitres (ml) and the standard deviation is 7.4 millilitres.

a) Discuss how the filling weights for the liquid detergent cartons are distributed. (rounded off to two decimals). [3]

b) What percentage of filled cartons will weigh between 447.8ml and 477.4ml? [3]

Question 3 [10]

Consider the following frequency table of distances travelled by 120 salesmen.

Class intervals
(distance travelled in kilometres) |
frequency (f) | Cumulative
frequency (F) |
Midpoint (m) | f x m | m2 | f x m^{2} |

400 -< 420 | 12 | 12 | 410 | 4920 | 168100 | 2017200 |

420 -< 440 | 27 | 39 | 430 | 11610 | 184900 | 4992300 |

440 -< 460 | 34 | 73 | 450 | 15300 | 202500 | 6885000 |

460 -< 480 | 24 | 97 | 470 | 11280 | 220900 | 5301600 |

480 -< 500 | 15 | 112 | 490 | 7350 | 240100 | 3601500 |

500 -< 520 | 8 | 120 | 510 | 4080 | 260100 | 2080800 |

120 |
54540 |
1276600 |
24878400 |

a) Calculate and interpret the mean and the median (rounded off to two decimals). [5]

b) Calculate the standard deviation (rounded off to two decimals). [3]

c) Calculate and interpret the skewness (rounded off to two decimals). [2]

Question 4 [7]

A study is conducted at a retirement home to determine the attitudes of nurses towards various administrative procedures. A sample of 13 nurses is selected from a total of 25 nurses employed by the retirement home.

a) How many different ways can 13 nurses be selected (rounded off to zero decimals)? [2]

b) Nine of the 25 nurses are male. If 13 nurses are randomly selected from those employed by the retirement home, what is the probability that the sample selected will include exactly 5 male and 8 female nurses (rounded off to three decimals)? [5]

Question 5 [3]

A car dealership has an exclusive area where they showcase their bestselling vehicles. This area can accommodate 14 luxury cars. If there are 3 Honda Civic’s, 4 Hyundai Tucson’s, 2 Jeep Wranglers, 3 Mercedes Benz and 2 BMW’s, in how many different ways can the cars be displayed in the exclusive area?

Question 6 [5]

A survey of magazine subscribers showed that during the past 12 months, 45.8% rented a car for business reasons, 54% rented a car for personal reasons, and 30% rented a car for both business and personal reasons.

a) What is the probability that a subscriber rented a car during the past 12 months for business or personal reasons (rounded off to three decimals)? [2]

b) What is the probability that a subscriber did not rent a car during the past 12 months for neither business nor personal reasons (rounded off to three decimals)? [1]

c) What is the probability that a subscriber rented a car during the past 12 months for personal reasons given that the subscriber rented a car for business reasons (rounded off to three decimals)?

[2]

Question 7 [5]

A market research company is hired to determine the commuting preferences of the people in a small town. There are two taxi companies competing for fares in the area (Brilliant Taxis and Taxi Ride Co.), but both offer different types of services. The initial analysis suggests that 1 in 5 people travel with Brilliant Taxis.

If ten randomly selected people are interviewed, then what is the probability that:

a) What is the probability that two or less people will prefer travelling with Brilliant Taxis (rounded off to three decimals)? [2]

b) What is the probability that between five and seven (inclusive) people will prefer travelling with Taxi Ride Co. (rounded off to three decimals)? [2]

If 1200 randomly selected people are interviewed, what would be the expected number of people who prefer Brilliant Taxis (rounded off to zero decimals)? [1]

Question 8 [5]

It is reported that households in the Atlantic Seaboard region of Cape Town spend an annual average of R48000 on groceries. Assume a normal distribution with a standard deviation of R11900.

a) What is the probability that a randomly selected Atlantic Seaboard region household spends more than R49428 on groceries annually (rounded off to three decimals)? [2]

b) What percentage of Atlantic Seaboard region households spend between R33125 and R54426 on groceries annually (rounded off to two decimals)? [3]

**Get completed answers on above questions on Statistics**

**Answer 1: **The calculation of mean, median and mode is performed as follows:

3850 | 3950 | 4050 | 3880 | 3755 | 3710 |

3890 | 4130 | 3940 | 4325 | 3920 | 3880 |

Mean is | 3940 |

Median is | 3905 |

Mode is | 3880 |

Get completed answers on above questions on statistics from the best experts of Student Life Saviour in South Africa.

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