"Denkopdrachten" Normaalverdeling

We write N(m,s) to denote a normal dist. with mean m and
standard deviation s.  So the IQ test is N(100,16) and 
Dutch men's height is N(181,6) (in cm).

Then make sure you can do the following.

1. Given N(100,16) convert the following to Z-scores:

  92, 132, 164, 90

2. Given N(181cm,6cm) convert the following heights to 
Z-scores:

  187 cm, 172 cm, 181 cm, 160 cm

3. Given N(100,16), what percentile do the following
scores fall on?

  108, 96, 120, 88

4. Given that Dutch women aged 18-24 jr. have a normal height
distribution with mean 172cm and sd 6cm, what percentage of 
them will have heights in the following range?

  a. between 166 cm and 178 cm  (abbreviated: 166 <= h <= 178)

  b. up to 175 cm (<= 175)

  c. more than 180 cm (> 180)

  d. 160 <= h <= 180

5. Only the "top p%" have a chance of winning a scholarship.

  a. What is the top 10% of a N(100,16) distribution?

  b. What is the top 5% of a N(500,100) distribution?

6. The bottom 5% of a satisfaction survey should be checked 
carefully.  The survey had a near normal distribution of 
N(3.1,0.7)   Which satisfaction scores will lead to further
checking?

7. Mass-market clothing manufacturers ignore the 5% of the 
population with extreme sizes (the 2.5% very small and 2.5% 
very large).  What consequences does this have in the 
following cases?

  a. Men's shoe size is N(43,2.5)  What men have to buy
  shoes in specialty shops?

  b. Women's hat size is N(6.75, 0.25).  Which women 
  are forced to buy expensive hats?