6 The heights of the female students at Breven college are normally distributed:
- \(90 \%\) of the female students have heights less than 182.7 cm .
- \(40 \%\) of the female students have heights less than 162.5 cm .
- Find the mean and the standard deviation of the heights of the female students at Breven college.
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Ten female students are chosen at random from those at Breven college.
Find the probability that fewer than 8 of these 10 students have heights more than 162.5 cm .