A study was made of adult men from region \(A\) of a country. It was found that their heights were normally distributed with a mean of 175.4 cm and standard deviation 6.8 cm .
Find the proportion of these men that are taller than 180 cm .
A student claimed that the mean height of adult men from region \(B\) of this country was different from the mean height of adult men from region \(A\).
A random sample of 52 adult men from region \(B\) had a mean height of 177.2 cm
The student assumed that the standard deviation of heights of adult men was 6.8 cm both for region \(A\) and region \(B\).
Use a suitable test to assess the student's claim.
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