Question

QUESTION 1 Which of the following statements is TRUE for a set of data which has a skewed distribution? Oa The median is the average of the Ob. The interquartile range is one half of Oc. The mean always lies between the Od. The median partitions the set of data smallest and the largest observation the range median and the mode into two equal parts QUESTION2 The distribution of the distance travelled by 35 people from an outer Brisbane suburb was found to be symmetrical. Five people who were previously travelling the longest distance moved further away andd travelled even further. If the distribution of distance travelled is recalculated using the new set of observations for the same sample of people, the shape of the new distribution: O a would remain symmetrical would be right skewed C. would be left skewed O d. is not able to be determined QUESTION 3 The human resource officer at a large university constructed the following table. It details the number of sick days in January taken by permanent employees. Number of sick days Percentage of staff 5 or more 0 1 2 3 4 70.5 15.47.9 2.30.3 If there were 688 permanent employees on the payroll, how many took more than one sick day during January? (round to the nearest whole number -please make sure to use conventional rounding rules ie round up if the decimal point in your answer is .5 or greater) QUESTION 4 The mean and standard deviation of a binomial distribution with n 25 and p 0.20 are 5 and 2 8 and 4 O 4 and 3 5 and 4 2 points Save Answer QUESTION 5 Students working part-time at the Gabba walk around the stands selling hot dogs and meat pies on commission. They know that the weather affects the value of sales. On a cold night, they can make $909 in sales, while on a cool night they can make $833 in sales. On a mild night they can make $695 in sales. If the probabilities for the first two scenarios are 0.15 and 0.34 respectively, then find the average value of sales in dollars. (two decimal places)

Answer 1

Solution:

1. When data is skewed, the first 3 options do not follow. That is, for a symmetric distribution, median is average of smallest and largest observation (and equals the mode, as well as mean of the distribution). Option (b) as well holds for a symmetrical distribution. For any skewed distribution, median lies between the mean and mode of the data. Finally, median partitions any data set into two equal parts, irrespective of distribution being symmetric or skewed. Thus, correct option is (d).

2. If the 5 people who had initially traveled the maximum, have traveled even more further, while remaining people's distance coverage remain same as before, the mean value of distance traveled will go slightly up. But the median distance traveled is still same as old, since distance of only top 5 people has increased. So, now mean > median, which is an indication that the new distribution is rightly skewed. So, correct option is (b) would be right skewed.

3. The percentage of staff taking more than 1 sick day = 100 - percentage of people taking less than or equal to 1 sick day

= 100 - (percentage taking 0 sick day + percentage taking 1 sick day)

= 100 - (70.5 + 15.4)

= 100 - 85.9 = 14.1%

So, with number of permanent employees = 688, required percentage = (14.1/100)*688 = 97.008

So, 97 (post-rounding off) employees took more than one sick day during January.

4. For a binomial distribution, mean = n*p and variance = n*p*(1-p)

So, here mean = 25*0.20 = 5

variance = 25*0.20*(1-0.20) = 4

Standard deviation = (variance)^1/2 = 4^1/2 = 2

So, correct option is (a) 5 and 2.

5. Since probabilities of all possible scenarios should add to 1,

probability of cold night + probability of cool night + probability of mild night = 1

0.15 + 0.34 + probability of mild night = 1

Probability of mild night = 1 - 0.15 - 0.34 = 0.51

Average sales value = probability of cold night*sales in cold night + probability of cool night*sales in cool night + probability of mild night*sales in mild night

Average value of sales = 0.15*909 + 0.34*833 + 0.51*695

Average sales value = 136.35 + 283.22 + 354.45 = $774.02

So, average sales in dollars is $774.02 (2 decimal places)