 # VZFEI. Statistics. Examination №4.

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VZFEI. All-Russian Correspondence Financial and Economic Institute.
The solution of problems of the control work №4 matematichekoy statistics.
E-book (DjVu-file) contains solutions 3-x control work tasks for students VZFEI. Solving problems presented in the form of a scanned handwriting collected into a single document of 20 pages. This document is stored in a format DjVu, which is open in Internet Explorer after installing utility program (plug-in). Link to download and install DjVu-plugin can be found on the company's homepage LIZARDTECH. DjVu-file that contains the conditions of tasks and their detailed solution completely and ready for viewing on your computer and print. All tasks were successfully offset VZFEI teachers.

Topics of problems of control work.
1. Under the scheme of self-repetitions of the random sample was selected from 100 students in 1500, and obtained data on their growth. Search:
a) The probability that the average height of all students differs from the average growth of students in the sample by no more than 2 cm. (in absolute value).
b) the boundaries in which the probability of 0.99 lies share of all students, the growth of which no more than 166 cm.
c) The volume of sample repetitions at which the same limits for the share (see. p. b) it can be ensured with a probability of 0.9606.

2. According to the task №1, using the chi-square test of Pearson, at a significance level a = 0,05 to test the hypothesis that the random variable X - increase student normal distribution. Build on one drawing a histogram of the empirical distribution and the corresponding normal curve.

3. Distribution of 40 banks in terms of interest rate X (%) and the size of the loans issued by the bank Y (mln. Rub.) Presented in the table below:
You need:
1) Calculate the group average and construct empirical regression line.
2) Assuming that between the variables X and Y there is a linear correlation
a) Find the equation of the regression lines, build their schedules on a drawing with empirical regression lines; give an economic interpretation of equations
b) Calculate the correlation coefficient at the level of significance of a = 0,05, to assess its value and draw a conclusion about distress and direction of the connection between the variables X and Y.
c) Using appropriate regression equation to determine the average size of the bank granted loans, the interest rate is equal to 15%. 