ANSWER TO FRAME 58.

a. = +1

b. = -2

FRAME 59.

Suppose we had evidence that the heights of recruits followed a normal distribution with a

mean of 175cm and a standard deviation of 6cm. We are interested in finding what percent of

the population of all recruits have heights between 175cm and 187cm. A diagram would look

like:

To answer the question we need to find the shaded area. We know there is a relationship

between the area under the normal curve and the distance along the horizontal base line

measured in standard deviations from the mean (or z"s).

The distance from u = 175cm to X = 187cm is 12cm. The value of one standard deviation is

σ = 6cm. Then the distance in question along the horizontal axis must be 12/6 = 2 standard

deviations from the mean, or z -2. We can formalize this thought process with the following

formula:

z= X= u

where,

σ

z = number of standard deviations from the mean.

u = mean of the population.

σ = standard deviation of the population

X = value of interest.

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