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Times - Mathematics - Exam, Exams of Mathematics

Aliah UniversityMathematics

This is the Exam of Mathematics which includes Vector, Scalar Product, Vector Product, Speed, Acceleration, Particle, Position, Magnitude, Same Direction etc. Key important points are: Times, Metres, Successive, Mean of the Time, Standard Deviation, Median, Three Events, Probabilities, Terms, Random Variable

Typology: Exams

2012/2013

Uploaded on 02/26/2013

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MATH 162 Introduction to Statistics
June Examination 2010
Time allowed: Two Hours and a Half
Instructions
Answer all questions in Section A.
The marks for the best three answers in Section B will be used in the assessment.
PAPER CODE MATH264 PAGE 1 OF 11 Continued
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MATH 162 Introduction to Statistics

June Examination 2010

Time allowed: Two Hours and a Half

Instructions

Answer all questions in Section A.

The marks for the best three answers in Section B will be used in the assessment.

SECTION A

  1. The times t (in seconds) taken by an athlete to run 400 metres on ten successive days were:

  2. 2 55. 7 54. 2 52. 7 53. 6 56. 8 54. 0 53. 7 59. 3 53. 8

(a) Calculate the mean of the times. [3 marks] (b) Calculate the standard deviation of the times. [3 marks] (c) Determine the median of the times. [2 marks]

  1. A random variable X has probability density function

f (x) =

Ax(6 − x)^2 0 ≤ x ≤ 6 0 elsewhere

(a) Find the value of the constant A. [2 marks] (b) Calculate (i) the mean; (ii) the variance; (iii) the standard deviation of X. [6 marks]

  1. The heights of men in a particular district are distributed with mean μ cm and standard deviation σ cm. On the basis of the results obtained from a random sample of 100 men from the district, the 95% confidence interval for μ was calculated and found to be (177.22 cm, 179.18 cm). Calculate

(a) the value of the sample mean, [4 marks] (b) the value of σ, [2 marks] (c) a symmetric 90% confidence interval for μ. [2 marks]

Section B

  1. Cows can become afflicted with a non-infectious disease irrespective of whether or not other cows are infected. Assume that seventy per cent of the herd have been treated by an injection that combats the disease but does not prevent its occurrence. The chances of recovery from the disease in one week are 1 in 20 if untreated and 1 in 5 if treated.

(a) If a cow has recovered within one week, what is the probability that the cow received the injection? [10 marks] (b) If a cow has not recovered within one week, what is the probability the cow received the injection? [10 marks]

  1. A can company believes that the number of breakdowns per 8-hour shift on its machine-operated assembly line follows a Poisson distribution with mean 1.1. Record- ing the numbers of breakdowns per shifts for 70 shifts, the following data were obtained. Number of breakdowns 0 1 2 3 ≥ 4 Number of shifts 16 22 18 14 0

(a) Test at the 5% level the hypothesis that these data are indeed drawn from a Poisson distribution with mean 1.1. [8 marks] (b) Using the data to estimate the mean number of breakdowns per shift. Test at the 5% level the hypothesis that the data are drawn from a Poisson distribution with the mean determined from the data. [12 marks]

  1. A number of different types of fungi are distributed at random in a field. 80% of these fungi are mushrooms, and the remainder are toadstools. 5% of the toadstools are poisonous. A man, who cannot distinguish between mushrooms and toadstools, wanders across the field and picks a total of 100 fungi. Determine, using Normal or Poisson appropriation as appropriate, the probability that the man has picked

(a) at least 20 toadstools, [10 marks] (b) exactly two poisonous toadstools. [10 marks]

  1. In a large factory, 60 workers were randomly selected and asked to give their opinion on a new pension scheme that their employers were hoping to introduce. The following Table can be formed:

Income Opinion on a New Pension Scheme In favour Undecided Against Totals High or Average 15 4 16 35 Low 2 10 13 25 Totals 17 14 29 60

(a) Find the expected frequencies according to the hypothesis that the opinions of the workers independent of their incomes. [8 marks] (b) Test at the 5% level whether the differences in the observed and expected data are significant. [12 marks]

PAPER CODE MATH264 PAGE 11 OF 11 End