Statistics and Probability Answers

In 12 test runs an experimental engine consumed on the average 12.9 gallons of gasoline per minute with a standard deviation of 1.6 gallons.
a) Construct a 90% confidence interval for the average gasoline consumption of the engine.
b) Construct a 95% confidence interval for the standard deviation.

There are 50 misprints in a book which has 250 pages.
a) What is the averages of misprints in one page?
b) Find the probability that randomly selected page has no misprints?
c) What is the probability that in randomly selected page there is at least one misprint?

A and B play 12 games of chess, of which 6 are won by A, 4 are won by B, and 2 end in a draw. They agree to play a match consisting of 3 games. Find the probability that
a) A wins all 3 games
b) 2 games end in a draw
c) A and B win alternately
d) B wins at least 1 game.

A doctor may administer drug A or drug B to her/his patients. Drug A is used on all
patients except for the 10 % that show an allergic reaction to the drug. Ninety percent of
the patients treated with drug A recover, while 70% of the patients treated with Drug B
recover. a) Find the probability that a person will be treated with Drug A and will
recover. b) a person will be treated with Drug B and will not recover

The summer monsoon rains in a country follow approximately a Normal distribution with mean 854 millimeters (mm) of rainfall and standard deviation 87 mm.
(b) "Normal rainfall" means within 20% of the long-term average, or between 683 mm and 1025 mm. In what percent of all years is the rainfall normal?

A class have 100 students
A : student study history is 0.4
B: student study math 0.5

a) calculate probability is that at least 1 student studied one of two subjects
b) calculate probability is that none of the students studied one of the two subjects
c) calculate probability is that 1 student study history, don't study math

What characteristics are important to process when considering a random sample?

For a normal distribution with mean,μ=2, and standard deviation, σ=4 what proportion of observations take values greater than 4?

QUESTION 3/SOALAN 3
Table 2: Mathematics Score/Jadual 2: Skor Matematik
27 37 30 28 39 25 45 28
32 28 26 38 31 30 47 41




a) Based on Table 2, organize the data into a frequency distribution by taking 25 as the lower limit of the first class and 5 as the class width. (4)
b) Construct a “less than or equal” ogive for the frequency distribution established in (a) and then approximate the number of candidates who scores below 35. (6)

QUESTION 1

Suppose you are working for a company in the music business. They make stereos, musical instruments and produce CD’s. They decide to do a survey on dance preferences by college students. Basically, they wanted to know about college students’ interests and practices on dance music. A survey was administered to a random sample of 37 students and recorded in Table 1:
A – Ironic dance B – Pro dance C – Sway dance
D – Dad-dance E – Twerk dance

Table 1
Male Female Male Female Male
A A A A E
C E C C A
A A C B E
A C A D D
A A B A A
C D E B B
D A D D A
D A




















Based on Table 1 in Question 1:
a) Prepare a multiple frequency table for dance preferences of both genders. (2)

b) Using your frequency table, draw a multiple bar chart to represent the information.
(4)
c) Briefly discuss and compare the percentage of favorite and least favorite dance preferences of both genders. (4)
[Total: 10 marks]