probability

Question

I don't know how to solve this 

 

The average weight of a nickel is 5 grams, with a standard deviation of 0.1 grams. What is the probability of opening a roll of 20 nickels and finding the average weight is greater than 5.01 grams?

The average weight of a nickel is 5 grams, with a standard deviation of 0.1 grams.  What is the probability of opening a roll of 20 nickels and finding the average weight is  greater than 5.01 grams?

Answer 1

Kenneth that is actually incorrect.

 

Your answer is not considering the average of 20 nickels being more than 5.01 grams  (What about the 20??)

 

Here is the full solution:

 

We must assume the distribution of nickel weights in the population is normally distributed becasue our sample is small, 20.

 

Therefore our sampling distribution of size 20 will be approximately normal.

 

The sampling distribution will be centered at 5. since the population is centered there.

 

However, the standard deviation of our sampling distribution is not .1 grams. It is .1/sqrt(20)

 

Our z = (5.01-5)/(.1/sqrt(20)) = .4472135955

 

The area above that z-score would be .327360445. This is the probabilty you are looking for

 

 

 

Answer 2

Assume that the average nickel from this package weighs 5.01 g

 

Use z = (x - μ) / σ for this instance, with the given mu and sigma values:

 

z = (5.01 - 5) / 0.1 = 0.01 / 0.1 = 0.1

 

From my trusty Standard Normal Distribution Table, the area under the curve for z = 0.1 is 0.53985 which means that the probability of an average coin from this package exceeding 5.01 would be 1 - 0.53985 = 0.46015