╨д╨╛╤А╨╝╤Г╨╗╨░ Z-╤В╨╡╤Б╤В╨░
╨д╨╛╤А╨╝╤Г╨╗╨░ ╨┤╨╗╤П ╤А╨░╤Б╤З╨╡╤В╨░ Z-╤В╨╡╤Б╤В╨░ ╨▓ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╡
Z-╤В╨╡╤Б╤В ╨▓ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╡ ╨╛╤В╨╜╨╛╤Б╨╕╤В╤Б╤П ╨║ ╨┐╤А╨╛╨▓╨╡╤А╨║╨╡ ╨│╨╕╨┐╨╛╤В╨╡╨╖╤Л, ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╨╝╨╛╨╣ ╨┤╨╗╤П ╨╛╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П ╤В╨╛╨│╨╛, ╤А╨░╨╖╨╗╨╕╤З╨░╤О╤В╤Б╤П ╨╗╨╕ ╤А╨░╤Б╤Б╤З╨╕╤В╨░╨╜╨╜╤Л╨╡ ╤Б╤А╨╡╨┤╨╜╨╕╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П ╨┤╨▓╤Г╤Е ╨▓╤Л╨▒╨╛╤А╨╛╨║ ╨▓ ╤Б╨╗╤Г╤З╨░╨╡, ╨╡╤Б╨╗╨╕ ╨┤╨╛╤Б╤В╤Г╨┐╨╜╤Л ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╤Л╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╤П ╨╕ ╨▓╤Л╨▒╨╛╤А╨║╨░ ╨▓╨╡╨╗╨╕╨║╨░.
Z = (╤Е тАУ ╨╝) / ╨Я╤А╨╕╨▓╨╡╤В
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╨│╨┤╨╡ x = ╨╗╤О╨▒╨╛╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ ╨╕╨╖ ╤Б╨╛╨▓╨╛╨║╤Г╨┐╨╜╨╛╤Б╤В╨╕
- ╬╝ = ╤Б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ ╨╜╨░╤Б╨╡╨╗╨╡╨╜╨╕╤П
- ╞б = ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ ╨╜╨░╤Б╨╡╨╗╨╡╨╜╨╕╤П
╨Т ╤Б╨╗╤Г╤З╨░╨╡ ╨▓╤Л╨▒╨╛╤А╨║╨╕ ╤Д╨╛╤А╨╝╤Г╨╗╨░ ╨┤╨╗╤П ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╕ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П Z-╤В╨╡╤Б╤В╨░ ╤А╨░╤Б╤Б╤З╨╕╤В╤Л╨▓╨░╨╡╤В╤Б╤П ╨┐╤Г╤В╨╡╨╝ ╨▓╤Л╤З╨╕╤В╨░╨╜╨╕╤П ╤Б╤А╨╡╨┤╨╜╨╡╨│╨╛ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П ╨▓╤Л╨▒╨╛╤А╨║╨╕ ╨╕╨╖ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П X. ╨Ч╨░╤В╨╡╨╝ ╤А╨╡╨╖╤Г╨╗╤М╤В╨░╤В ╨┤╨╡╨╗╨╕╤В╤Б╤П ╨╜╨░ ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ ╨▓╤Л╨▒╨╛╤А╨║╨╕. ╨Ь╨░╤В╨╡╨╝╨░╤В╨╕╤З╨╡╤Б╨║╨╕ ╤Н╤В╨╛ ╨┐╤А╨╡╨┤╤Б╤В╨░╨▓╨╗╤П╨╡╤В ╨║╨░╨║
Z = (╤Е тАУ x_╤Б╤А╨╡╨┤╨╜╨╡╨╡) / ╤Б
╨│╨┤╨╡
- x = ╨╗╤О╨▒╨╛╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ ╨╕╨╖ ╨▓╤Л╨▒╨╛╤А╨║╨╕
- ╤Е_╤Б╤А╨╡╨┤╨╜╨╡╨╡ = ╨▓╤Л╨▒╨╛╤А╨╛╤З╨╜╨╛╨╡ ╤Б╤А╨╡╨┤╨╜╨╡╨╡
- s = ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ ╨▓╤Л╨▒╨╛╤А╨║╨╕
╨Ю╨│╨╗╨░╨▓╨╗╨╡╨╜╨╕╨╡
╨а╨░╤Б╤З╨╡╤В Z-╤В╨╡╤Б╤В╨░ (╤И╨░╨│ ╨╖╨░ ╤И╨░╨│╨╛╨╝)
╨д╨╛╤А╨╝╤Г╨╗╨░ ╨┤╨╗╤П ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╕ Z-╤В╨╡╤Б╤В╨░ ╨┤╨╗╤П ╨╜╨░╤Б╨╡╨╗╨╡╨╜╨╕╤П ╨▓╤Л╨▓╨╛╨┤╨╕╤В╤Б╤П ╤Б ╨╕╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╨╜╨╕╨╡╨╝ ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╤Е ╤И╨░╨│╨╛╨▓:
- ╨Т╨╛-╨┐╨╡╤А╨▓╤Л╤Е, ╨▓╤Л╤З╨╕╤Б╨╗╨╕╤В╨╡ ╤Б╤А╨╡╨┤╨╜╨╕╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П ╤Б╨╛╨▓╨╛╨║╤Г╨┐╨╜╨╛╤Б╤В╨╕ ╨╕ ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ ╨╜╨░ ╨╛╤Б╨╜╨╛╨▓╨╡ ╨╜╨░╨▒╨╗╤О╨┤╨╡╨╜╨╕╤П, ╨╖╨░╤Д╨╕╨║╤Б╨╕╤А╨╛╨▓╨░╨╜╨╜╨╛╨│╨╛ ╨▓ ╤Б╤А╨╡╨┤╨╜╨╡╨╝ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╕ ╤Б╨╛╨▓╨╛╨║╤Г╨┐╨╜╨╛╤Б╤В╨╕, ╨╕ ╨║╨░╨╢╨┤╨╛╨╡ ╨╜╨░╨▒╨╗╤О╨┤╨╡╨╜╨╕╨╡ ╨╛╨▒╨╛╨╖╨╜╨░╤З╨░╨╡╤В╤Б╤П xi. ╨в╨╛╨│╨┤╨░ ╨╛╨▒╤Й╨╡╨╡ ╨║╨╛╨╗╨╕╤З╨╡╤Б╤В╨▓╨╛ ╨╜╨░╨▒╨╗╤О╨┤╨╡╨╜╨╕╨╣ ╨▓ ╨┐╨╛╨┐╤Г╨╗╤П╤Ж╨╕╨╕ ╨╛╨▒╨╛╨╖╨╜╨░╤З╨░╨╡╤В╤Б╤П ╤З╨╡╤А╨╡╨╖ N.
╨б╤А╨╡╨┤╨╜╤П╤П ╤З╨╕╤Б╨╗╨╡╨╜╨╜╨╛╤Б╤В╤М ╨╜╨░╤Б╨╡╨╗╨╡╨╜╨╕╤П,
╨б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ ╨╜╨░╤Б╨╡╨╗╨╡╨╜╨╕╤П,
- ╨Э╨░╨║╨╛╨╜╨╡╤Ж, ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨░ Z-╤В╨╡╤Б╤В╨░ ╨▓╤Л╤З╨╕╤Б╨╗╤П╨╡╤В╤Б╤П ╨┐╤Г╤В╨╡╨╝ ╨▓╤Л╤З╨╕╤В╨░╨╜╨╕╤П ╤Б╤А╨╡╨┤╨╜╨╡╨│╨╛ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П ╤Б╨╛╨▓╨╛╨║╤Г╨┐╨╜╨╛╤Б╤В╨╕ ╨╕╨╖ ╨┐╨╡╤А╨╡╨╝╨╡╨╜╨╜╨╛╨╣. ╨Ч╨░╤В╨╡╨╝ ╤А╨╡╨╖╤Г╨╗╤М╤В╨░╤В ╨┤╨╡╨╗╨╕╤В╤Б╤П ╨╜╨░ ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ ╨│╨╡╨╜╨╡╤А╨░╨╗╤М╨╜╨╛╨╣ ╤Б╨╛╨▓╨╛╨║╤Г╨┐╨╜╨╛╤Б╤В╨╕, ╨║╨░╨║ ╨┐╨╛╨║╨░╨╖╨░╨╜╨╛ ╨╜╨╕╨╢╨╡.
Z = (╤Е тАУ ╨╝╨║) /
╨д╨╛╤А╨╝╤Г╨╗╨░ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╕ Z-╤В╨╡╤Б╤В╨░ ╨┤╨╗╤П ╨▓╤Л╨▒╨╛╤А╨║╨╕ ╨┐╨╛╨╗╤Г╤З╨░╨╡╤В╤Б╤П ╨╕╨╖ ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╤Е ╤И╨░╨│╨╛╨▓:
- ╨Т╨╛-╨┐╨╡╤А╨▓╤Л╤Е, ╤А╨░╤Б╤Б╤З╨╕╤В╨░╨╣╤В╨╡ ╤Б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ ╨▓╤Л╨▒╨╛╤А╨║╨╕ ╨╕ ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ ╤В╨░╨║ ╨╢╨╡, ╨║╨░╨║ ╤Г╨║╨░╨╖╨░╨╜╨╛ ╨▓╤Л╤И╨╡. ╨Ч╨┤╨╡╤Б╤М ╨╛╨▒╤Й╨╡╨╡ ╨║╨╛╨╗╨╕╤З╨╡╤Б╤В╨▓╨╛ ╨╜╨░╨▒╨╗╤О╨┤╨╡╨╜╨╕╨╣ ╨▓ ╨▓╤Л╨▒╨╛╤А╨║╨╡ ╨╛╨▒╨╛╨╖╨╜╨░╤З╨░╨╡╤В╤Б╤П n ╤В╨░╨║╨╕╨╝ ╨╛╨▒╤А╨░╨╖╨╛╨╝, ╤З╤В╨╛ n < N.
╨Т╤Л╨▒╨╛╤А╨╛╤З╨╜╨╛╨╡ ╤Б╤А╨╡╨┤╨╜╨╡╨╡,
╨б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ ╨▓╤Л╨▒╨╛╤А╨║╨╕,
- ╨Э╨░╨║╨╛╨╜╨╡╤Ж, ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨░ Z-╤В╨╡╤Б╤В╨░ ╤А╨░╤Б╤Б╤З╨╕╤В╤Л╨▓╨░╨╡╤В╤Б╤П ╨┐╤Г╤В╨╡╨╝ ╨▓╤Л╤З╨╕╤В╨░╨╜╨╕╤П ╤Б╤А╨╡╨┤╨╜╨╡╨│╨╛ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П ╨▓╤Л╨▒╨╛╤А╨║╨╕ ╨╕╨╖ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П X. ╨Ч╨░╤В╨╡╨╝ ╤А╨╡╨╖╤Г╨╗╤М╤В╨░╤В ╨┤╨╡╨╗╨╕╤В╤Б╤П ╨╜╨░ ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ ╨▓╤Л╨▒╨╛╤А╨║╨╕, ╨║╨░╨║ ╨┐╨╛╨║╨░╨╖╨░╨╜╨╛ ╨╜╨╕╨╢╨╡.
Z = (x — x_mean) / ╤Б
╨Я╤А╨╕╨╝╨╡╤А╤Л
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╨Я╤А╨╕╨╝╨╡╤А тДЦ1
╨Я╤А╨╡╨┤╨┐╨╛╨╗╨╛╨╢╨╕╨╝, ╤З╤В╨╛ ╨▓ ╤И╨║╨╛╨╗╨╡ ╨╡╤Б╤В╤М ╤Г╤З╨░╤Й╨╕╨╡╤Б╤П, ╤П╨▓╨╕╨▓╤И╨╕╨╡╤Б╤П ╨╜╨░ ╨║╨╗╨░╤Б╤Б╨╜╤Л╨╣ ╤В╨╡╤Б╤В. ╨б╤А╨╡╨┤╨╜╨╕╨╣ ╨▒╨░╨╗╨╗ ╨▓ ╤В╨╡╤Б╤В╨╡ тАФ 75, ╨░ ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ тАФ 15. ╨Э╨╛ ╤Б╨╜╨░╤З╨░╨╗╨░ ╨╛╨┐╤А╨╡╨┤╨╡╨╗╨╕╤В╨╡ Z-╤В╨╡╤Б╤В ╨Ф╤Н╨▓╨╕╨┤╨░, ╨║╨╛╤В╨╛╤А╤Л╨╣ ╨╜╨░╨▒╤А╨░╨╗ 90 ╨▒╨░╨╗╨╗╨╛╨▓.
╨Ф╨░╨╜╨╜╤Л╨╣
- ╨б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ ╨╜╨░╤Б╨╡╨╗╨╡╨╜╨╕╤П, ╬╝ = 75
- ╨б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ ╨╜╨░╤Б╨╡╨╗╨╡╨╜╨╕╤П, ╞б = 15
╨б╨╗╨╡╨┤╨╛╨▓╨░╤В╨╡╨╗╤М╨╜╨╛, ╨╝╨╛╨╢╨╜╨╛ ╤А╨░╤Б╤Б╤З╨╕╤В╨░╤В╤М ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╤Г Z-╤В╨╡╤Б╤В╨░ ╨║╨░╨║
Z = (90 тАУ 75) / 15
╨б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨░ Z-╤В╨╡╤Б╤В╨░ ╨▒╤Г╨┤╨╡╤В тАУ
- Z = 1
╨в╨░╨║╨╕╨╝ ╨╛╨▒╤А╨░╨╖╨╛╨╝, ╤А╨╡╨╖╤Г╨╗╤М╤В╨░╤В ╤В╨╡╤Б╤В╨░ ╨Ф╤Н╨▓╨╕╨┤╨░ ╨╜╨░ ╨╛╨┤╨╜╨╛ ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ ╨▓╤Л╤И╨╡ ╤Б╤А╨╡╨┤╨╜╨╡╨│╨╛ ╨▒╨░╨╗╨╗╨░ ╨│╨╡╨╜╨╡╤А╨░╨╗╤М╨╜╨╛╨╣ ╤Б╨╛╨▓╨╛╨║╤Г╨┐╨╜╨╛╤Б╤В╨╕, ╤В. ╨╡. ╨▓ ╤Б╨╛╨╛╤В╨▓╨╡╤В╤Б╤В╨▓╨╕╨╕ ╤Б z-╨╛╤Ж╨╡╨╜╨║╨╛╨╣. ╨┤╨░╨╜╨╜╤Л╨╡, ╨║╨╛╤В╨╛╤А╤Л╨╡ ╨┐╨╛╨╝╨╛╨│╨░╤О╤В ╨┐╤А╨╛╨▓╨╡╤А╨╕╤В╤М ╤А╨░╤Б╤Б╨╝╨░╤В╤А╨╕╨▓╨░╨╡╨╝╤Г╤О ╨│╨╕╨┐╨╛╤В╨╡╨╖╤Г. ╨Ф╤А╤Г╨│╨╕╨╝╨╕ ╤Б╨╗╨╛╨▓╨░╨╝╨╕, ╤Н╤В╨╛ ╤А╨░╤Б╤Б╤В╨╛╤П╨╜╨╕╨╡ ╤В╨╛╤З╨║╨╕ ╨┤╨░╨╜╨╜╤Л╤Е ╨╛╤В ╤Б╤А╨╡╨┤╨╜╨╡╨│╨╛ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П ╨│╨╡╨╜╨╡╤А╨░╨╗╤М╨╜╨╛╨╣ ╤Б╨╛╨▓╨╛╨║╤Г╨┐╨╜╨╛╤Б╤В╨╕, ╨▓╤Л╤А╨░╨╢╨╡╨╜╨╜╨╛╨╡ ╨║╨░╨║ ╨║╤А╨░╤В╨╜╨╛╨╡ ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╝╤Г ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╤О. 84,13% ╤Г╤З╨░╤Й╨╕╤Е╤Б╤П ╨╜╨░╨▒╤А╨░╨╗╨╕ ╨╝╨╡╨╜╤М╤И╨╡ ╨▒╨░╨╗╨╗╨╛╨▓, ╤З╨╡╨╝ ╨Ф╤Н╨▓╨╕╨┤.
╨Я╤А╨╕╨╝╨╡╤А #2
╨Т╨╛╨╖╤М╨╝╨╡╨╝, ╨║ ╨┐╤А╨╕╨╝╨╡╤А╤Г, 30 ╤Б╤В╤Г╨┤╨╡╨╜╤В╨╛╨▓, ╨╛╤В╨╛╨▒╤А╨░╨╜╨╜╤Л╤Е ╨▓ ╨║╨░╤З╨╡╤Б╤В╨▓╨╡ ╤З╨░╤Б╤В╨╕ ╨▓╤Л╨▒╨╛╤А╨╛╤З╨╜╨╛╨╣ ╨│╤А╤Г╨┐╨┐╤Л, ╨╛╨┐╤А╨╛╤И╨╡╨╜╨╜╨╛╨╣, ╤З╤В╨╛╨▒╤Л ╤Г╨╖╨╜╨░╤В╤М, ╤Б╨║╨╛╨╗╤М╨║╨╛ ╨║╨░╤А╨░╨╜╨┤╨░╤И╨╡╨╣ ╨╛╨╜╨╕ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╨╗╨╕ ╨╖╨░ ╨╜╨╡╨┤╨╡╨╗╤О. ╨Ю╨┐╤А╨╡╨┤╨╡╨╗╨╕╤В╤М ╨▒╨░╨╗╨╗ Z-╤В╨╡╤Б╤В╨░ ╨┤╨╗╤П 3-╨│╨╛ ╤Г╤З╨╡╨╜╨╕╨║╨░ ╨╜╨░ ╨╛╤Б╨╜╨╛╨▓╨╡ ╨┤╨░╨╜╨╜╤Л╤Е ╨╛╤В╨▓╨╡╤В╨╛╨▓: 3, 2, 5, 6, 4, 7, 4, 3, 3, 8, 3, 1, 3, 6, 5, 2, 4 , 3, 6, 4, 5, 2, 2, 4, 4, 2, 8, 3, 6, 7.
╨Ф╨░╨╜╨╜╤Л╨╣,
- x = 5, ╤В╨░╨║ ╨║╨░╨║ ╨╛╤В╨▓╨╡╤В ╤В╤А╨╡╤В╤М╨╡╨│╨╛ ╤Г╤З╨╡╨╜╨╕╨║╨░ ╤А╨░╨▓╨╡╨╜ 5
- ╨Ю╨▒╤К╨╡╨╝ ╨▓╤Л╨▒╨╛╤А╨║╨╕, n = 30
╨Т╤Л╨▒╨╛╤А╨╛╤З╨╜╨╛╨╡ ╤Б╤А╨╡╨┤╨╜╨╡╨╡, = (3 + 2 + 5 + 6 + 4 + 7 + 4 + 3 + 3 + 8 + 3 + 1 + 3 + 6 + 5 + 2 + 4 + 3 + 6 + 4 + 5 + 2 + 2 + 4 + 4 + 2 + 8 + 3 + 6 + 7) / 30
╨б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ = 4,17
╨Ь╨╛╨╢╨╜╨╛ ╤А╨░╤Б╤Б╤З╨╕╤В╨░╤В╤М ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ ╨▓╤Л╨▒╨╛╤А╨║╨╕, ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╤П ╨┐╤А╨╕╨▓╨╡╨┤╨╡╨╜╨╜╤Г╤О ╨▓╤Л╤И╨╡ ╤Д╨╛╤А╨╝╤Г╨╗╤Г.
╤Н = 1,90
╨б╨╗╨╡╨┤╨╛╨▓╨░╤В╨╡╨╗╤М╨╜╨╛, ╨╝╨╛╨╢╨╜╨╛ ╤А╨░╤Б╤Б╤З╨╕╤В╨░╤В╤М ╨▒╨░╨╗╨╗ Z-╤В╨╡╤Б╤В╨░ ╨┤╨╗╤П ╤В╤А╨╡╤В╤М╨╡╨│╨╛ ╤Г╤З╨╡╨╜╨╕╨║╨░ ╨║╨░╨║:
Z = (╤Е тАУ ╤Е) / ╤Б
- Z = (5 тАУ17) / 1,90
- Z = 0,44
╨в╨░╨║╨╕╨╝ ╨╛╨▒╤А╨░╨╖╨╛╨╝, ╨╕╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╨╜╨╕╨╡ 3-╨╝ ╤Г╤З╨░╤Й╨╕╨╝╤Б╤П ╨▓ 0,44 ╤А╨░╨╖╨░ ╨┐╤А╨╡╨▓╤Л╤И╨░╨╡╤В ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ ╨┐╨╛ ╤Б╤А╨░╨▓╨╜╨╡╨╜╨╕╤О ╤Б╨╛ ╤Б╤А╨╡╨┤╨╜╨╕╨╝ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡╨╝ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╨╜╨╕╤П ╨▓╤Л╨▒╨╛╤А╨║╨╕, ╤В. ╨╡. ╤Б╨╛╨│╨╗╨░╤Б╨╜╨╛ ╤В╨░╨▒╨╗╨╕╤Ж╨╡ Z-╨┐╨╛╨║╨░╨╖╨░╤В╨╡╨╗╨╡╨╣, 67% ╤Г╤З╨░╤Й╨╕╤Е╤Б╤П ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╤О╤В ╨╝╨╡╨╜╤М╤И╨╡ ╨║╨░╤А╨░╨╜╨┤╨░╤И╨╡╨╣, ╤З╨╡╨╝ 3-╨╣ ╤Г╤З╨░╤Й╨╕╨╣╤Б╤П.
╨Я╤А╨╕╨╝╨╡╤А тДЦ3
╨Т╨╛╨╖╤М╨╝╨╡╨╝, ╨║ ╨┐╤А╨╕╨╝╨╡╤А╤Г, 30 ╤Б╤В╤Г╨┤╨╡╨╜╤В╨╛╨▓, ╨╛╤В╨╛╨▒╤А╨░╨╜╨╜╤Л╤Е ╨▓ ╨║╨░╤З╨╡╤Б╤В╨▓╨╡ ╤З╨░╤Б╤В╨╕ ╨▓╤Л╨▒╨╛╤А╨╛╤З╨╜╨╛╨╣ ╨│╤А╤Г╨┐╨┐╤Л, ╨║╨╛╤В╨╛╤А╨░╤П ╨┐╤А╨╛╨▓╨╡╨╗╨░ ╨╛╨┐╤А╨╛╤Б, ╤З╤В╨╛╨▒╤Л ╤Г╨╖╨╜╨░╤В╤М, ╤Б╨║╨╛╨╗╤М╨║╨╛ ╨║╨░╤А╨░╨╜╨┤╨░╤И╨╡╨╣ ╨▒╤Л╨╗╨╛ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╨╜╨╛ ╨╖╨░ ╨╜╨╡╨┤╨╡╨╗╤О. ╨Ю╨┐╤А╨╡╨┤╨╡╨╗╨╕╤В╤М ╨▒╨░╨╗╨╗ Z-╤В╨╡╤Б╤В╨░ ╨┤╨╗╤П 3-╨│╨╛ ╤Г╤З╨╡╨╜╨╕╨║╨░ ╨╜╨░ ╨╛╤Б╨╜╨╛╨▓╨╡ ╨┤╨░╨╜╨╜╤Л╤Е ╨╛╤В╨▓╨╡╤В╨╛╨▓: 3, 2, 5, 6, 4, 7, 4, 3, 3, 8, 3, 1, 3, 6, 5, 2, 4 , 3, 6, 4, 5, 2, 2, 4, 4, 2, 8, 3, 6, 7.
╨Э╨╕╨╢╨╡ ╨┐╤А╨╕╨▓╨╡╨┤╨╡╨╜╤Л ╨┤╨░╨╜╨╜╤Л╨╡ ╨┤╨╗╤П ╤А╨░╤Б╤З╨╡╤В╨░ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╕ Z-╤В╨╡╤Б╤В╨░.
╨Т╤Л ╨╝╨╛╨╢╨╡╤В╨╡ ╨╛╨▒╤А╨░╤В╨╕╤В╤М╤Б╤П ╨║ ╨╗╨╕╤Б╤В╤Г Excel ╨╜╨╕╨╢╨╡ ╨┤╨╗╤П ╨┐╨╛╨┤╤А╨╛╨▒╨╜╨╛╨│╨╛ ╤А╨░╤Б╤З╨╡╤В╨░ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╕ Z-╤В╨╡╤Б╤В╨░.
╨Р╨║╤В╤Г╨░╨╗╤М╨╜╨╛╤Б╤В╤М ╨╕ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╨╜╨╕╨╡
╨Т╨░╨╢╨╜╨╛ ╨┐╨╛╨╜╨╕╨╝╨░╤В╤М ╨║╨╛╨╜╤Ж╨╡╨┐╤Ж╨╕╤О ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╕ Z-╤В╨╡╤Б╤В╨░, ╨┐╨╛╤В╨╛╨╝╤Г ╤З╤В╨╛ ╨╛╨╜╨░ ╨╛╨▒╤Л╤З╨╜╨╛ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╤В╤Б╤П ╨▓╤Б╤П╨║╨╕╨╣ ╤А╨░╨╖, ╨║╨╛╨│╨┤╨░ ╨▓╨╛╨╖╨╜╨╕╨║╨░╤О╤В ╤Б╨┐╨╛╤А╤Л ╨╛ ╤В╨╛╨╝, ╤Б╨╗╨╡╨┤╤Г╨╡╤В ╨╗╨╕ ╤В╨╡╤Б╤В╨╛╨▓╨░╤П ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨░ ╨╜╨╛╤А╨╝╨░╨╗╤М╨╜╨╛╨╝╤Г ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤О. ╨╝╨╛╨╢╨╡╤В ╨╜╨░╤Е╨╛╨┤╨╕╤В╤М╤Б╤П ╨▓ ╨╖╨░╨┤╨░╨╜╨╜╨╛╨╝ ╨┤╨╕╨░╨┐╨░╨╖╨╛╨╜╨╡, ╨┐╤А╨╕ ╤Н╤В╨╛╨╝ ╨▒╨╛╨╗╤М╤И╨░╤П ╤З╨░╤Б╤В╤М ╨╛╨▒╨╗╨░╤Б╤В╨╕ ╤А╨░╤Б╨┐╤А╨╛╤Б╤В╤А╨░╨╜╨╡╨╜╨╕╤П ╨╜╨░╤Е╨╛╨┤╨╕╤В╤Б╤П ╨▓ ╤Б╨╡╤А╨╡╨┤╨╕╨╜╨╡, ╨░ ╨╜╨╡╨╝╨╜╨╛╨│╨╕╨╡ — ╨▓ ╤Е╨▓╨╛╤Б╤В╨░╤Е, ╨╜╨░ ╨║╤А╨░╨╣╨╜╨╕╤Е ╤В╨╛╤З╨║╨░╤Е. ╨н╤В╨╛ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡ ╨╕╨╝╨╡╨╡╤В ╨┤╨▓╨░ ╨║╨╗╤О╤З╨╡╨▓╤Л╤Е ╨┐╨░╤А╨░╨╝╨╡╤В╤А╨░: ╤Б╤А╨╡╨┤╨╜╨╡╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╨╡ (┬╡) ╨╕ ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ (╧Г), ╨║╨╛╤В╨╛╤А╤Л╨╡ ╨╕╨│╤А╨░╤О╤В ╨║╨╗╤О╤З╨╡╨▓╤Г╤О ╤А╨╛╨╗╤М ╨▓ ╤А╨░╤Б╤З╨╡╤В╨╡ ╨┤╨╛╤Е╨╛╨┤╨╜╨╛╤Б╤В╨╕ ╨░╨║╤В╨╕╨▓╨╛╨▓ ╨╕ ╨▓ ╤Б╤В╤А╨░╤В╨╡╨│╨╕╨╕ ╤Г╨┐╤А╨░╨▓╨╗╨╡╨╜╨╕╤П ╤А╨╕╤Б╨║╨░╨╝╨╕. ╨Я╨╛╨┤╤А╨╛╨▒╨╜╨╡╨╡ ╤З╨╕╤В╨░╨╣╤В╨╡ ╨▓ ╤Б╨╛╨╛╤В╨▓╨╡╤В╤Б╤В╨▓╤Г╤О╤Й╨╡╨╣ ╨╜╤Г╨╗╨╡╨▓╨╛╨╣ ╨│╨╕╨┐╨╛╤В╨╡╨╖╨╡. ╨Ю╨┤╨╜╨░╨║╨╛ ╤Б╨╗╨╡╨┤╤Г╨╡╤В ╨┐╨╛╨╝╨╜╨╕╤В╤М, ╤З╤В╨╛ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╤В╤М Z-╤В╨╡╤Б╤В ╨╝╨╛╨╢╨╜╨╛ ╤В╨╛╨╗╤М╨║╨╛ ╨▓ ╤В╨╛╨╝ ╤Б╨╗╤Г╤З╨░╨╡, ╨╡╤Б╨╗╨╕ ╤А╨░╨╖╨╝╨╡╤А ╨▓╤Л╨▒╨╛╤А╨║╨╕ ╨┐╤А╨╡╨▓╤Л╤И╨░╨╡╤В 30. ╨Т ╨┐╤А╨╛╤В╨╕╨▓╨╜╨╛╨╝ ╤Б╨╗╤Г╤З╨░╨╡ ╨╝╨╛╨╢╨╜╨╛ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╤В╤М t-╤В╨╡╤Б╤ВT-╤В╨╡╤Б╤В╨в-╤В╨╡╤Б╤В тАФ ╤Н╤В╨╛ ╨╝╨╡╤В╨╛╨┤ ╨╛╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П ╤В╨╛╨│╨╛, ╨╛╤В╨╗╨╕╤З╨░╤О╤В╤Б╤П ╨╗╨╕ ╤Б╤А╨╡╨┤╨╜╨╕╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П ╨┤╨▓╤Г╤Е ╨│╤А╤Г╨┐╨┐ ╨┤╤А╤Г╨│ ╨╛╤В ╨┤╤А╤Г╨│╨░. ╤Б╤Г╤Й╨╡╤Б╤В╨▓╨╡╨╜╨╜╨╛. ╨н╤В╨╛ ╨╝╨╡╤В╨╛╨┤ ╨╗╨╛╨│╨╕╤З╨╡╤Б╨║╨╛╨╣ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╕, ╨╛╨▒╨╗╨╡╨│╤З╨░╤О╤Й╨╕╨╣ ╨┐╤А╨╛╨▓╨╡╤А╨║╤Г ╨│╨╕╨┐╨╛╤В╨╡╨╖. ╨Я╨╛╨┤╤А╨╛╨▒╨╜╨╡╨╡.
╨а╨╡╨║╨╛╨╝╨╡╨╜╨┤╤Г╨╡╨╝╤Л╨╡ ╤Б╤В╨░╤В╤М╨╕
╨н╤В╨░ ╤Б╤В╨░╤В╤М╤П ╨┐╤А╨╡╨┤╤Б╤В╨░╨▓╨╗╤П╨╡╤В ╤Б╨╛╨▒╨╛╨╣ ╤А╤Г╨║╨╛╨▓╨╛╨┤╤Б╤В╨▓╨╛ ╨┐╨╛ ╤Д╨╛╤А╨╝╤Г╨╗╨╡ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╕ Z-Test. ╨Ч╨┤╨╡╤Б╤М ╨╝╤Л ╤Г╨╖╨╜╨░╨╡╨╝, ╨║╨░╨║ ╤А╨░╤Б╤Б╤З╨╕╤В╨░╤В╤М Z-╤В╨╡╤Б╤В ╨▓ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╨║╨╡, ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╤П ╨╡╨│╨╛ ╤Д╨╛╤А╨╝╤Г╨╗╤Г, ╨┐╤А╨╕╨╝╨╡╤А╤Л ╨╕ ╨╖╨░╨│╤А╤Г╨╢╨░╨╡╨╝╤Л╨╣ ╤И╨░╨▒╨╗╨╛╨╜ Excel. ╨Т╤Л ╨╝╨╛╨╢╨╡╤В╨╡ ╤Г╨╖╨╜╨░╤В╤М ╨▒╨╛╨╗╤М╤И╨╡ ╨╛ ╤Д╨╕╨╜╨░╨╜╤Б╨╛╨▓╨╛╨╝ ╨░╨╜╨░╨╗╨╕╨╖╨╡ ╨╕╨╖ ╤Б╨╗╨╡╨┤╤Г╤О╤Й╨╕╤Е ╤Б╤В╨░╤В╨╡╨╣:
- Z-╤В╨╡╤Б╤В ╨┐╤А╨╛╤В╨╕╨▓ T-TestZ-╤В╨╡╤Б╤В ╨┐╤А╨╛╤В╨╕╨▓. T-╤В╨╡╤Б╤В Z-╤В╨╡╤Б╤В тАФ ╤Н╤В╨╛ ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╤З╨╡╤Б╨║╨░╤П ╨│╨╕╨┐╨╛╤В╨╡╨╖╨░, ╨║╨╛╤В╨╛╤А╨░╤П ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╤В╤Б╤П ╨┤╨╗╤П ╨╛╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П ╤В╨╛╨│╨╛, ╤А╨░╨╖╨╗╨╕╤З╨░╤О╤В╤Б╤П ╨╗╨╕ ╤А╨░╤Б╤Б╤З╨╕╤В╨░╨╜╨╜╤Л╨╡ ╤Б╤А╨╡╨┤╨╜╨╕╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П ╨┤╨▓╤Г╤Е ╨▓╤Л╨▒╨╛╤А╨╛╨║, ╨║╨╛╨│╨┤╨░ ╨┤╨╛╤Б╤В╤Г╨┐╨╜╨╛ ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ ╨╕ ╤А╨░╨╖╨╝╨╡╤А ╨▓╤Л╨▒╨╛╤А╨║╨╕ ╨▓╨╡╨╗╨╕╨║. ╨б ╨┤╤А╤Г╨│╨╛╨╣ ╤Б╤В╨╛╤А╨╛╨╜╤Л, T-╤В╨╡╤Б╤В ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╤В╤Б╤П ╨┤╨╗╤П ╨╛╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П ╤В╨╛╨│╨╛, ╨╜╨░╤Б╨║╨╛╨╗╤М╨║╨╛ ╤Б╤А╨╡╨┤╨╜╨╕╨╡ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П ╤А╨░╨╖╨╗╨╕╤З╨╜╤Л╤Е ╨╜╨░╨▒╨╛╤А╨╛╨▓ ╨┤╨░╨╜╨╜╤Л╤Е ╨╛╤В╨╗╨╕╤З╨░╤О╤В╤Б╤П ╨┤╤А╤Г╨│ ╨╛╤В ╨┤╤А╤Г╨│╨░, ╨║╨╛╨│╨┤╨░ ╤Б╤В╨░╨╜╨┤╨░╤А╤В╨╜╨╛╨╡ ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ ╨╕╨╗╨╕ ╨┤╨╕╤Б╨┐╨╡╤А╤Б╨╕╤П ╨╜╨╡╨╕╨╖╨▓╨╡╤Б╤В╨╜╤Л.╨Я╨╛╨┤╤А╨╛╨▒╨╜╨╡╨╡
- ╨д╨╛╤А╨╝╤Г╨╗╨░ ╤А╨░╨╖╨╝╨╡╤А╨░ ╨▓╤Л╨▒╨╛╤А╨║╨╕╨д╨╛╤А╨╝╤Г╨╗╨░ ╤А╨░╨╖╨╝╨╡╤А╨░ ╨▓╤Л╨▒╨╛╤А╨║╨╕╨д╨╛╤А╨╝╤Г╨╗╨░ ╤А╨░╨╖╨╝╨╡╤А╨░ ╨▓╤Л╨▒╨╛╤А╨║╨╕ ╨╛╤В╤А╨░╨╢╨░╨╡╤В ╤Б╨╛╨╛╤В╨▓╨╡╤В╤Б╤В╨▓╤Г╤О╤Й╨╕╨╣ ╨┤╨╕╨░╨┐╨░╨╖╨╛╨╜ ╨│╨╡╨╜╨╡╤А╨░╨╗╤М╨╜╨╛╨╣ ╤Б╨╛╨▓╨╛╨║╤Г╨┐╨╜╨╛╤Б╤В╨╕, ╨▓ ╨║╨╛╤В╨╛╤А╨╛╨╣ ╨┐╤А╨╛╨▓╨╛╨┤╨╕╤В╤Б╤П ╤Н╨║╤Б╨┐╨╡╤А╨╕╨╝╨╡╨╜╤В ╨╕╨╗╨╕ ╨╛╨┐╤А╨╛╤Б. ╨Ю╨╜ ╨╕╨╖╨╝╨╡╤А╤П╨╡╤В╤Б╤П ╤Б ╨╕╤Б╨┐╨╛╨╗╤М╨╖╨╛╨▓╨░╨╜╨╕╨╡╨╝ ╤А╨░╨╖╨╝╨╡╤А╨░ ╤Б╨╛╨▓╨╛╨║╤Г╨┐╨╜╨╛╤Б╤В╨╕, ╨║╤А╨╕╤В╨╕╤З╨╡╤Б╨║╨╛╨│╨╛ ╨╖╨╜╨░╤З╨╡╨╜╨╕╤П ╨╜╨╛╤А╨╝╨░╨╗╤М╨╜╨╛╨│╨╛ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╤П ╨┐╤А╨╕ ╤В╤А╨╡╨▒╤Г╨╡╨╝╨╛╨╝ ╤Г╤А╨╛╨▓╨╜╨╡ ╨┤╨╛╤Б╤В╨╛╨▓╨╡╤А╨╜╨╛╤Б╤В╨╕, ╨┤╨╛╨╗╨╕ ╨▓╤Л╨▒╨╛╤А╨║╨╕ ╨╕ ╨┐╤А╨╡╨┤╨╡╨╗╨░ ╨┐╨╛╨│╤А╨╡╤И╨╜╨╛╤Б╤В╨╕.╨Я╨╛╨┤╤А╨╛╨▒╨╜╨╡╨╡
- ╨д╨╛╤А╨╝╤Г╨╗╨░ F-╤В╨╡╤Б╤В╨░╨д╨╛╤А╨╝╤Г╨╗╨░ F-╤В╨╡╤Б╤В╨░╨д╨╛╤А╨╝╤Г╨╗╨░ F-╤В╨╡╤Б╤В╨░ ╨╕╤Б╨┐╨╛╨╗╤М╨╖╤Г╨╡╤В╤Б╤П ╨┤╨╗╤П ╨▓╤Л╨┐╨╛╨╗╨╜╨╡╨╜╨╕╤П ╤Б╤В╨░╤В╨╕╤Б╤В╨╕╤З╨╡╤Б╨║╨╛╨│╨╛ ╤В╨╡╤Б╤В╨░, ╨║╨╛╤В╨╛╤А╤Л╨╣ ╨┐╨╛╨╝╨╛╨│╨░╨╡╤В ╤З╨╡╨╗╨╛╨▓╨╡╨║╤Г, ╨┐╤А╨╛╨▓╨╛╨┤╤П╤Й╨╡╨╝╤Г ╤В╨╡╤Б╤В, ╨╛╨┐╤А╨╡╨┤╨╡╨╗╨╕╤В╤М, ╨╕╨╝╨╡╤О╤В ╨╗╨╕ ╨┤╨▓╨░ ╨╜╨░╨▒╨╛╤А╨░ ╨┐╨╛╨┐╤Г╨╗╤П╤Ж╨╕╨╣, ╨║╨╛╤В╨╛╤А╤Л╨╡ ╨╕╨╝╨╡╤О╤В ╨╜╨╛╤А╨╝╨░╨╗╤М╨╜╨╛╨╡ ╤А╨░╤Б╨┐╤А╨╡╨┤╨╡╨╗╨╡╨╜╨╕╨╡ ╤В╨╛╤З╨╡╨║ ╨┤╨░╨╜╨╜╤Л╤Е, ╨╛╨┤╨╕╨╜ ╨╕ ╤В╨╛╤В ╨╢╨╡ ╤Б╤В╨░╨╜╨┤╨░╤А╤В. ╨╛╤В╨║╨╗╨╛╨╜╨╡╨╜╨╕╨╡ ╨╕╨╗╨╕ ╨╜╨╡╤В.╨Я╨╛╨┤╤А╨╛╨▒╨╜╨╡╨╡
- ╨д╨╛╤А╨╝╤Г╨╗╨░ ╨░╤Б╨╕╨╝╨╝╨╡╤В╤А╨╕╨╕
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