Question

Last year, the revenue for medical equipment companies had a mean of 70 million dollars with a standard deviation of 13 million. Find the percentage of companies with revenue between 50 million ánd 90 million dollars. Assume that the distribution is normal. Round your answer to the nearest hundredth.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the percentage of companies with revenue between 50 million and 90 million dollars, we need to calculate the z-scores for both revenue figures using the formula:

z = (X - μ) / σ

Where:
X = Revenue figure
μ = Mean revenue (70 million dollars)
σ = Standard deviation (13 million dollars)

For X = 50 million:
z1 = (50 - 70) / 13
z1 = -20 / 13
z1 ≈ -1.54

For X = 90 million:
z2 = (90 - 70) / 13
z2 = 20 / 13
z2 ≈ 1.54

Next, we can use a standard normal distribution table or a calculator to find the percentage of companies within these z-scores.

For z = -1.54, the area under the curve to the left of this score is approximately 0.0618 or 6.18%.

For z = 1.54, the area under the curve to the left of this score is approximately 0.9382 or 93.82%.

Therefore, the percentage of companies with revenue between 50 million and 90 million dollars is approximately 93.82% - 6.18% = 87.64%.

Rounded to the nearest hundredth, the percentage is 87.64%.