Variant 20

1. The probability of hit in a target by the first shooter is 0,8, and by the second shooter – 0,7. The shooters have shot simultaneously. What is the probability that only one of them hit in the target?

2. 1100 of 2000 tubes belong to the first batch, 650 – to the second, and 250 – to the third. 7% of the first batch, 6% of the second and 8% of the third are defective tubes. One tube is chosen at random. Determine the probability that the chosen tube is defective.

3. It has been established by long observations that 14 days at April are on the average rainy in Chicago. What is the probability that 5 of 7 randomly chosen days of the month will be rainy?

4. Let X be a discrete random variable distributed under the following law:

X	0	1	2	3	4	5
р	0,14	0,18	0,06	0,3	0,04	0,28

Find: a) the mathematical expectation and the dispersion of the random variable X; b) the probability of the following event: 1 < X  3.

5. A random variable X is given by the density of distribution f(x) = A(3x – x²) in the interval (0; 2), and f(x) = 0 outside of the interval. Find:

а) parameter A;

b) the mathematical expectation and the dispersion of the variable X.

6. A detail made by an automatic device is recognized suitable if the deviation of its controllable weight from the design one does not exceed 15 g. Random deviations of the controllable weight from the design one are subordinated to a normal law with dispersion 16 and mathematical expectation 20 g. How many percents of suitable details does the automatic device produce?

7. Estimate the probability that the absolute value of the deviation of the average height of 500 persons from the mathematical expectation of a random variable expressing the height of each person will not exceed 1 cm, assuming that the dispersion of each of these random variables does not exceed 7.

8. The following data on strength of a metal cable of a given batch have been received after testing 60 samples:

709	707	738	735	726	738	702	734	774	785
761	787	757	769	728	755	736	749	725	736
768	759	736	782	716	766	741	752	754	753
774	777	713	759	753	743	746	761	765	755
771	732	748	766	759	739	749	751	731	768
713	717	752	795	792	751	765	746	775	773

1) Compose the interval and the discrete variation series taking the beginning of the first interval equal 700, and the width of each interval equal 10.

2) Construct the histogram and the polygon of relative frequencies of distribution.

3) Find the mode and the median (using the discrete series).

4) Find empirical functions of distribution of continuous and discrete variation series; and construct their graphs.