Final answer:
The probability that a sample of 1530-second commercials costs more than $5 million is approximately 99.865%.
Step-by-step explanation:
To find the probability that a sample of 15 30-second commercials costs more than $5 million, we need to use the z-score formula:
z = (x - μ) / σ
Where x is the value we're interested in, μ is the mean, and σ is the standard deviation. In this case, x = $5 million, μ = $6.5 million, and σ = $0.5 million.
By substituting these values into the formula, we get:
z = ($5 million - $6.5 million) / $0.5 million = -3
Next, we need to find the area to the left of the z-score of -3 using a standard normal distribution table or calculator. This area represents the probability of a sample of commercials costing less than $5 million, so we subtract it from 1 to find the probability of the sample costing more than $5 million.
Finally, we have:
Probability = 1 - P(z < -3)
Using a standard normal distribution table or calculator, we can find that the area to the left of -3 is approximately 0.00135.
Therefore, the probability that a sample of 15 30-second commercials costs more than $5 million is approximately 1 - 0.00135 = 0.99865, or 99.865%.