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A company's marketing manager believes that the sales for next year will follow normal distribution with mean of $500.000 and standard deviation of $20.000

Calculate the probability that the sales will be less than $450.000 next year

User Jimiyash
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1 Answer

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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.

User TheCoolDrop
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