Question

What is the probability that the average sales over 12 randomly selected days will be between 1550 and 1700

Answer 1

To calculate the probability of the average sales falling between 1550 and 1700 over 12 randomly selected days, we need information about the distribution of sales. Assuming a normal distribution, we need the population mean (μ) and standard deviation (σ).

Let's say μ = 1600 and σ = 100. The standard error of the mean (SEM) is calculated as
`(\sigma)/(\sqrt n)`, where n is the sample size (12 in this case).

`SEM = (100)/(\sqrt12) \approx 28.87`

Now, calculate the z-scores for 1550 and 1700 using the formula
`z = ((X - \mu))/(SEM)`:

For
`X = 1550: z = ((1550 - 1600))/(28.87) \approx -1.73`

`X = 1700: z = ((1700 - 1600))/(28.87) \approx 3.46`

Look up these z-scores in the standard normal distribution table. The probability between -1.73 and 3.46 is approximately 0.9066.

Therefore, the probability that the average sales over 12 randomly selected days will be between 1550 and 1700 is approximately 90.66%.