Statistics and Probability Answers

Q1.Four cards are drawn at random from a pack of 52 cards. Find the probability that this consists
of:
a. a king, a queen, a jack and an ace.
b.two red and two blacks
c.two are kings and two are queens
d.there are two cards of hearts and two cards of diamonds

Q2.In shuffling a pack of cards four are accidentally dropped,find the chance that the missing cards should be one from each suit.

Q3.If the letters of the word regulations be arranged at random what is the probability that there will be exactly 4 letters between r and e.

A researcher wishes to test the claim of a particular cereal manufacturer that the mean weight of cereal in the boxes is less than 300g. A sample of 50 boxes yields a sample mean weight of 296g. Assume that the population standard deviation is 5g

Categorising a group of employees as working on site (in the office) and working from home
is an example of ______ scale of measurement.
1. nominal
2. ordinal
3. interval
4. ratio

A professor of History is teaching a section of 100 students. Her first exam’s grade distribution follows.
Exam grades

Frequency

45 to < 50

1

50 to < 55

2

55 to < 60

6

60 to < 65

19

65 to < 70

12

70 to < 75

22

75 to < 80

12

80 to < 85

13

85 to < 90

11

90 to < 95

0

95 to < 100

2

Calculate the standard deviation for this grouped data.

As part of a conservation project, Kojo Nyamekye was asked to measure the circumference of trees that were growing at different distances from the Winneba beach. His results are shown in the table below.

Distance (x)m
6
14
20
25
35
48
46
48
52

Circumference (y)cm
52
57
57
68
65
70
75
80
82

Given Σy2 = 41,700 Σxy = 21, 139

On graph paper, draw a scatter diagram to show Kojo’s results. Use a scale of 1 cm to represent 5m on the x-axis and 1cm to represent 10cm on the y-axis.

Calculate the mean distance, , of the trees from the beach.

Work out the mean circumference, , of the trees.

Plot and label the point M(, ) on your graph.

Find the equation of the regression line y on x, for Akosua’s results.

Draw the regression line y on x on your graph.

Use the equation of the regression line y on x to estimate the circumference of a tree that is 42 m from the beach.

The weights of bags of chips produced by Baaba’s Snacks has a bell-shaped distribution with a mean of 20 ounces and a standard deviation of 0.07 ounces.
Use this information to answer questions 7, 8 and 9.

Approximately 68% of chips bags weigh between:

Approximately what percentage of chips bags weigh between 19.86 and 20.07 ounces?


If 200 chips bags are selected at random, about how many do you expect to weigh more than 20.14 ounces?

In 1984, the 51 states in a country recorded a mean and median dropout rate of 26.5% and 25.3% respectively. Interpret the 1984 median dropout rate.

If a test was generally very easy, except for a few students who had very low scores, then the shape of the distribution of scores would be .......

Find the standard deviation of the set of data below.
y + 1, y + 2, y + 5, y + 9, y + 8.


Many professional schools require applicants to take a standardized test. Suppose 1000 students write the test, and your mark of 63 (out of 100) was the 73rd percentile. What does this mean?

A large college class is graded on a total points system. The total points earned in a semester by the students in the class vary normally with a mean of 675 and a standard deviation of 50. Another large class in a different department is graded on a 0 to 100 scale. The final grades in that class follow a normal model with a mean of 82 and a standard deviation of 6. Aseda earns 729 points in the first class, while Ayeyi scores 90 in the second class. Which student did better and why?

Samples of size 2 are taken from the population 1, 2, 3, 4, 5, 6 with replacement. Find
the following.
(i) The mean of population
(ii) S.D of the population
(iii) The mean of the sampling distribution of means
(iv) The S.D of the sampling distribution of means.