Question

Suppose the diameter of a particular car component follows the normal distribution with a mean 12 millimeters.and a standard deviation of 2.5 millimetres)

One of these car components is randomly selected and the diameter is measured. Find the z-value associated with each of the following desired probabilities (make sure to draw/label an appropriate picture for each part; only include the relevant numbers on each picture):
Find the z-value that represents the 7301 percentile.

Answer 1

To find the z-value for the 73.01 percentile in a normal distribution with a mean of 12 mm and a standard deviation of 2.5 mm, one would consult a z-table or statistical software to find the z-score corresponding to the area of 0.7301.

Step-by-step explanation:

To find the z-value that corresponds to the 73.01 percentile (or the 0.7301 probability level) for a normally distributed variable, we would use a z-table or statistical software. Since the area under the curve to the left of the desired z-value is 0.7301, we look up this area in the cumulative area column of the z-table to find the corresponding z-value.

Finding the z-value for the 73.01 percentile:

• Look up the closest area to 0.7301 in the z-table.
• Find the z-value that corresponds to this area.

Once the z-value has been determined, it can be interpreted as the number of standard deviations the measurement is from the mean. In this case, a diameter that falls at the 73.01 percentile is that many standard deviations above the mean diameter of 12 millimeters.