Search & Filtering
(a) At a large firm, there is a movement to form a union. Approximately 50% of the entire firm favour unionising, while 30% do not favour unionising. A pro-union leader takes a random sample of 100 workers. Let p1 denote the proportion in this sample that favours a union. An antiunion leader takes an independent random sample of 100 workers. Let p2 denote the proportion in this sample that favours the union. Calculate the probability that p1 exceeds p2 by 0.1 or more. (b) The mean annual income of statisticians of firm 1 is K10, 000 higher than the mean annual income of statisticians of a second firm. Random samples of size n1 = 100 and n2 = 200, respectively, are taken from the two firms. (i) What is the probability that in the two samples the mean annual incomes differ by more than K15, 000? For each firm (population), the standard deviation is K30, 000.
Consider the following data:
62 61 83 92 67 89 83 50 80 69 95 50 73 71 73 88 66 89 73 51 58 86 73 57 67 80 59 86 62 95 63 88 59 64 54 78 84 77 71 82 82 83 81 97 60 85 61 55 80 72
Make frequency distribution using 5 classes and find the following:
Arithmetic Mean
Median
Mode
All quartiles
3rd Deciles
46th Percentile
Coefficient of Skewness
Semi Inter Quartile Range (SIQR)
Standard Deviation
Mean Deviation
Variance
Sketch Histogram
Sketch OGIVE
we have 3 blue and 5 red balls lay in a box three balls are chosen randomly out of the box find the probability distribution for number of blue balls without replacement.
A company decides to check on the accuracy of invoicing. Invoices are prepared by Alicia, Linda
and Jane. A sample of 500 invoices are selected. Two hundred were prepared by Alicia, 120
by Linda and 180 by Jane. The error rates by Alicia, Linda and jane were found to be 25, 3%
and 4% respectively. From the sample of 500 invoices, one invoice was selected.
a) Draw a tree diagram for the above information
b) What is the probability that the invoice contains an error?
c) What is the probability that the invoice was prepared by Alicia, given that it contains no
error?
Q) Consider the following ungrouped data:
41 46 7 46 32 5 14 28 48 49 8 49 48 25 41 8 22 46 40 48
Find the following:
a) Arithmetic mean
b) Geometric mean
c) Harmonic mean
d) Median
e) Mode
f) Range
g) Mean deviation
h) Variance
i) Standard Deviation
if four coins are tossed once, which is not a possible value of the random variable for the number of heads?
Q) Consider the following ungrouped data:
41 46 7 46 32 5 14 28 48 49 8 49 48 25 41 8 22 46 40 48
Find the following:
a) Arithmetic mean
b) Geometric mean
c) Harmonic mean
d) Median
e) Mode
f) Range
g) Mean deviation
h) Variance
i) Standard Deviation
2. A Bank manager asked 10 of her bank tailors how many cash deposits they had received in the last 12 months. Their answers were as follows: 12, 23, 19, 6, 10, 7, 15, 25, 21, 12. Prepare a stem and leaf plot for these data. 3. Fifteen people were asked how often they drove to work over 10 working days. The number of times each person drove was as follows: 5, 7, 9, 9, 3, 5, 1, 0, 0, 4, 3, 7, 2, 9, 8 Make an ordered stem and leaf plot for this table.
A study found that 28% of car owners in Fiji had their cars washed professionally rather than do it themselves. If 18 car owners are randomly selected, find the probability that at most two people have their cars washed professionally.
A report in LTO stated that the average age of taxis in the Philippines is 12 years. An operations manager of a large taxi company selects a sample of 40 taxis and finds the average age of the taxis is 11.2 years. The standard deviation of the population is 2.3 years. At level of significance of 0.05, can it be concluded that the average age of the taxis in his company is less than the national average? In a clean white sheet of paper, State the hypotheses, the level of significance and critical region, compute for the value of one sample z test, write your decision rule and conclusion.
