Final answer:
To calculate the probability of sales being less than $450,000, first determine the Z-score for $450,000 based on the given normal distribution, then look up this Z-score in the standard normal distribution table or calculate it using a normal distribution function.
Step-by-step explanation:
The student has asked for the probability that the sales will be less than $450,000 next year, given that the sales are normally distributed with a mean of $500,000 and a standard deviation of $20,000.
To solve this, we use a standard normal distribution (also known as the Z-distribution) where the mean (μ) is 0 and the standard deviation (σ) is 1.
To find the required probability, we first calculate the Z-score for $450,000:
Z = (X - μ) / σ = ($450,000 - $500,000) / $20,000 = -2.5
Now we look up the Z-score in the standard normal distribution table or use a calculator with a normal distribution function, to find the probability corresponding to Z = -2.5. This gives us the probability of sales being less than $450,000.
Since tables and calculator outputs vary, I do not provide an exact number. However, the student can find the probability by looking up a Z-score of -2.5 in the standard normal distribution table or by using an appropriate calculator function.