You measure weekly sales. You can assume

Rami Masri

Rami Masri

Answered question

2022-03-27

You measure weekly sales. You can assume that weekly sales are normally distributed with mean 60 and standard deviation 18, and that weekly sales are independent across weeks.

 

What is the probability that AVERAGE WEEKLY sales over the next 4 weeks are below 66 in 4 decimal positions?

Answer & Explanation

nick1337

nick1337

Expert2023-04-26Added 777 answers

Given that the weekly sales are normally distributed with a mean (μ) of 60 and a standard deviation (σ) of 18. We are required to find the probability that the AVERAGE WEEKLY sales over the next 4 weeks are below 66.
Let X¯ be the sample mean of the weekly sales for the next 4 weeks. We know that the distribution of sample means follows a normal distribution with a mean of μ and a standard deviation of σn, where n is the sample size.
Here, n = 4, μ = 60 and σ = 18. Therefore, the standard deviation of the sample mean is σn=184=9.
We need to find P(X¯<66), which is the same as finding the z-score corresponding to a sample mean of 66 and then finding the area under the normal distribution curve to the left of that z-score.
z=X¯μσn=6660184=69=0.6667
Using a standard normal distribution table, we can find that P(Z<0.6667)=0.7475, where Z is a standard normal variable.
Therefore, the probability that the AVERAGE WEEKLY sales over the next 4 weeks are below 66 is 0.7475 or 0.7475 (rounded to 4 decimal places).

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