Hi,
mean of 176 cm and a standard deviation of 7 cm
182 cm, z = 6/7, < than 1 SD from mean, agree with You.
between
a. 155 cm and 197 cm? between 3 SDs from mean ⇒ 99.7%
b. 169 cm and 183 cm? between 1 SD from mean ⇒ 68% (sometimes 68.3 is used)
For the normal distribution:
one standard deviation from the mean accounts for about 68% of the set
two standard deviations from the mean account for about 95%
and three standard deviations from the mean account for about 99.7%.
Important to Understand z -values as they relate to the Standard Normal curve:
Below: z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.
Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and %50 to the right