Final answer:
To find the proportion of the population that is less than 20, we need to calculate the z-score for 20 and then use a standard normal distribution table. From the table, we find that the proportion of the population that is less than 20 is approximately 0.9474.
Step-by-step explanation:
To find the proportion of the population that is less than 20, we need to calculate the z-score for 20 and then use a standard normal distribution table.
The formula for calculating the z-score is: z = (x - μ) / σ, where x is the value we are interested in, μ is the population mean, and σ is the standard deviation.
Plugging in the values from the question, we get: z = (20 - 7) / 8 = 1.625. Now we can look up the z-value of 1.625 in the standard normal distribution table to find the proportion.
From the table, we find that the proportion of the population that is less than 20 is approximately 0.9474.