Question

The manufacturer of a certain brand of hot dogs claims that the mean fat content per hot dog is 20 grams. Suppose the standard deviation of the population of these hot dogs is 1.9 grams. A sample of these hot dogs is tested, and the mean fat content per hot dog of this sample is found to be 20.5 grams. Find the probability that the sample mean is at least 20.5 when the sample size is 35.

Answer 1

`z=(20.5-20)/((1.9)/(√(35)))= 1.557`

And using the normal standard distribution and the complement rule we got:

`P(z>1.557) =1-P(z<1.557) = 1-0.940 = 0.06`

Explanation:

For this case we define our random variable X as "fat content per hot dog" and we know the following parameters:

`\mu = 20, \sigma =1.9`

We select a sample of n=35 and we want to find the following probability:

`P(\bar X>20.5)`

For this case since the sample size is >30 we can use the central limit theorem and we use the z score formula given by:

`z=(\bar X -\mu)/((\sigma)/(√(n)))`

Replacing we got:

`z=(20.5-20)/((1.9)/(√(35)))= 1.557`

And using the normal standard distribution and the complement rule we got:

`P(z>1.557) =1-P(z<1.557) = 1-0.940 = 0.06`