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                      Basic Statistics Exam                                    

(2 Hours)

Question 1:

a) The price earnings ratios for 21 stocks in the retail trade category are:

8.3  9.6  9.5  9.1  8.8  11.2  7.7  10.1  9.9  10.8  10.2  8.0  8.4  8.1  11.6  9.6  8.8  8.0  10.4

9.8  9.2

   Organize this information into stem-and-leaf display.

   a) How many values are less than 9.0?

   b) List the values in the 10.0 up to 10.9 category.

   c) What is the middle value? 

   d) What are the largest and smallest price earnings ratios?

b) The following is the frequency distribution of the selling prices of 80 vehicles:

   1 - Construct a less than cumulative frequency polygon. Fifty percent of the vehicles were sold for less than what amount?

   2 - Calculate the mean selling price (x bar), median and the mode. Illustrate their relative positions graphically.

   3 - Calculate the coefficient of skewness and the coefficient of variation.

Question 2:

1 - Compute  the geometric mean of the following values: 8, 12, 14, 26, 5.

2- If A1 and A2 are two events on the sample space S such that:

   P(A1 U A2) = 0.80  ,    P(A1) = 0.35

  Find each of the following:

     a) P(Ā1 ∩ A2)

     b) P(A2) in the following two cases:

             i - A1 and A2 are mutually exclusive.

            ii- A1and A2 are independent.

Question 3:

1) Compute the mean and the variance of the following discrete probability distribution :

          and then compute    i) E (2X+3)        ii) V(3X - 1)

2) In a binomial distribution  n = 8, π = 0.30, find the following probabilities:

              a) X = 2    ,      b) X ≤ 2     ,       c) X ≥ 3

3) Suppose a population consists of 15 items 5 of which are defective . A sample of 3 items is selected without replacement. What is the probability that exactly 2 are defective?

4) If x ~ N (70, 10). Calculate:

        a) P ( x > 80)         b) P (60 ≤ X < 100).

        c) P ( x  ≥   74), where x bar is the arithmetic mean of a sample of size 25 observations randomly selected from the population.

Question 4:

1- From a population of size N = 100, a sample of size n = 9 is  selected from which is formed that:

      Σ x = 540,     Σ x²  = 33200

construct the 95% confidence interval for the population mean.