SOLUTION: Kingston Electronics, inc., offers a “no hassle” returns policy. The number of items returned per day follows the normal distribution. The mean number of customer returns is 10

Question 1192832: Kingston Electronics, inc., offers a “no hassle” returns policy. The number of items returned per day follows the normal distribution. The mean number of customer returns is 10.3 per day and the standard deviation is 2.25 per day.
1)The probability that the number of returns exceed a particular amount of 5%. What is the number of returns?
I did the following:
n= (z*std/Error)^2
(1.645* 2.25/.05)^2
Please assist me.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

This problem is not asking for the min sample size.

Instead, your teacher wants to know the value of k such that P(Z > k) = 0.05
The value of k itself is not the answer but it will lead to it.
The Z refers to the standard normal distribution variable. It's a very special normal bell curve with mean = 0 and standard deviation = 1.

Use a table such as this
https://www.ztable.net/
or similar found in your textbook to find that P(Z < -1.65) = 0.04947 which is close enough to 0.05

Due to symmetry, P(Z > 1.65) = 0.04947 = 0.05

Use this as the z score to find the corresponding raw score x.
z = (x-mu)/sigma
z*sigma = x-mu
x = mu+z*sigma
x = 10.3 + 1.65*2.25
x = 14.0125
This rounds to x = 14

So P(X > 14) = 0.05 approximately when X follows a normal distribution with mu = 10.3 and sigma = 2.25, which is the mean and standard deviation respectively.

The number of returns in the set {14, 15, 16, ...} constitutes the top 5% of all returns.

Answer: 14

Side note: you can use a calculator such as this one
https://davidmlane.com/normal.html
to make the process much quicker, but I have a feeling your teacher will want you to use a Z table and/or show some semblance of the steps done.
Of course, it's best to ask your teacher which methods are allowed.
The calculator is at least a good way to check your work as shown in the screenshot below.

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