Variant 10

1. Three dice are tossed. Find the probability that the sum of landed aces of the dice is divided on 5.

2. A collector has received 4 boxes of details made by the first factory, and 3 boxes of details made by the second factory. The probability that a detail of the first factory is standard is equal to 0,75; the second factory – 0,85. Find the probability that a randomly extracted detail from a randomly chosen box will be standard (collector – сборщик).

3. There is a group of 60 persons born at April. Find the probability that the birthday for three persons will be the first of April. Assume that the probability of a birth in a fixed day of April is equal to 1/30.

4. The probability that a book necessary for a student is available in a library is equal to 0,4. Compose the law of distribution of the number of libraries which will be visited by the student if there are five libraries in the city.

5. The distribution function of a continuous random variable X is given by:

Find: 1) the density of distribution; 2) the mathematical expectation and the dispersion of X; 3) the probability of hit of the random variable X into the interval (0; /8).

6. A random variable X is normally distributed with mathematical expectation M(X) = 12 and dispersion D(X) = 4. Find the probability that:

а) X will take on a value belonging to the interval (7; 14);

b) X will differ from the mathematical expectation less than on 1,5.

7. The dispersion of each of 1000 independent random variables does not exceed 4. Estimate the probability that the arithmetic mean of these random variables will differ from the arithmetic mean of their mathematical expectations less than on 0,15.

8. There are the following data on monthly volume of cigarettes (in thousand packs) of 100 supermarkets:

32	87	52	61	52	64	79	67	58	46
58	53	83	31	56	50	65	47	58	77
53	47	51	70	40	54	53	26	13	55
6	86	73	56	1	69	62	39	49	77
48	66	53	51	78	66	52	63	53	88
68	16	31	74	45	49	66	80	95	93
69	14	56	41	76	60	42	51	49	74
28	45	62	55	43	51	54	66	67	63
68	52	48	72	34	40	64	17	56	69
21	25	35	37	54	33	45	37	45	28

1) Compose the interval and the discrete variation series taking the beginning of the first interval equal 0, 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.