Problem 2
According to the Empirical Rule, roughly 95% of the normal distribution is within 2 standard deviations of the mean.
So the value 108 is 2 standard deviations above the mean, while 76 is 2 standard deviations below the mean.
The distance between those values is 108-76 = 32 units. Divide by 4 to get 32/4 = 8 to indicate the standard deviation itself. I'm dividing by 4 because we add the "2 standard deviations" to itself twice which is a total of 4 standard deviations in distance.
You could also solve like this
z = (x-mu)/sigma
2 = (108-92)/sigma
2 = 16/sigma
2sigma = 16
sigma = 16/2
sigma = 8
There's a similar set of steps if you were to use z = -2 and x = 76, which should lead to sigma = 8 as well.
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Problem 3
The center of the distribution is at point c, and that's 170, since that's given to us. The center is always the mean.
The standard deviation is 7. Each tickmark on that horizontal number line shown represents a full standard deviation (aka 7 cm). This means going from c to d will lead to
d = c + sigma = 170+7 = 177
and
e = d + sigma = 177+7 = 184
or you could say
e = c+2*sigma = 170+2*7 = 184
To determine the other values, we go backwards by subtracting off multiples of sigma.
a = c - 3*sigma = 170 - 3*7 = 170 - 21 = 149
b = c - 1*sigma = 170 - 1*7 = 170 - 7 = 163
