the distribution of sale price (online) for four-year-old harley davidson touring motorcycles is approximately normally distributed with a mean of $14,000 and a standard deviation of $4,000. a) mr. mayo plans to spend between $9,000 and $12,000 on a motorcycle. what proportion of the available motorcycles of this type can he afford?

A Z-score is a needs to be measured that describes the relationship of a value to the mean of a set of values.
The Z-score is expressed in standard deviations of the mean.
A Z-score of 0 signifies that the data point is entirely score is the same as the mean score.

The data for the sale price (online) for four-year-old harley davidson touring motorcycles is given.

The formula for the z score is-

Z = (x - μ)/σ

In which,

Find z score for x = $9,000.

z($9,000) = (9,000 - 14000)/4000

z($9,000) = -1.25

Find the p value from obtained z from negative z table.

p($9,000) = z(-1.25)

p($9,000) = 0.1056

For x = $12,000

z($12,000) = (12,000 - 14000)/4000

z($12,000) = -0.5

Find the p value from obtained z

p($9,000) = z(-0.5)

p($9,000) = 0.3085

For p($9,000 < x < $12,000) = 0.3085 - 0.1056

p($9,000 < x < $12,000) = 0.2029

p($9,000 < x < $12,000) = 20.29%

Thus, the proportion of the available motorcycles of sale price (online) for four-year-old harley davidson touring motorcycles is 20.29%.

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