Normal Distribution and Acceptable Strips: Calculating the Proportion

To find the proportion of acceptable strips, we need to find the area under the normal distribution curve between 98cm and 103cm.

First, we need to calculate the standard deviation (σ) using the variance given:

Standard deviation (σ) = √variance = √2.25 = 1.5 cm

Next, we can use the formula for the standard normal distribution:

z = (x - μ) / σ

where z is the z-score, x is the value of the strip, μ is the mean, and σ is the standard deviation.

For the lower bound:
z1 = (98 - 100) / 1.5 = -2/1.5 = -1.33

For the upper bound:
z2 = (103 - 100) / 1.5 = 3/1.5 = 2

We can then use a standard normal distribution table or a calculator to find the corresponding proportions.

Using a standard normal distribution table, we find that the proportion of strips below 98cm (z < -1.33) is approximately 0.0918.

Similarly, the proportion of strips below 103cm (z < 2) is approximately 0.9772.

To find the proportion of strips between 98cm and 103cm, we subtract the proportion below 98cm from the proportion below 103cm:

Proportion = 0.9772 - 0.0918 = 0.8854

Therefore, approximately 88.54% of the strips produced by the machine are acceptable.