Question

The weights of beagles have a mean of 25 pounds and a standard deviation of 3 pounds. A random sample of 50 beagles is collected. What is the probability that a sample of this size has a mean weight below 26 pounds?

Answer 1

`z =(26-25)/((3)/(√(50)))= 2.357`

And we can find the probability using the normal distribution table and we got:

`P(z<2.357) =0.9908`

Explanation:

Let X the random variable of interest and we can find the parameters:

`\mu =25, \sigma= 3`

And for this case we select a sample size n =50. And since the sample size is higher than 30 we can use the central limit theorem and the distribution for the sample mean would be given by:

`\bar X \sim N(\mu, (\sigma)/(√(n)))`

We want to find the following probability:

`P(\bar X <26)`

And we can use the z score formula given by:

`z =(\bar X -\mu)/((\sigma)/(√(n)))`

And replacing we got:

`z =(26-25)/((3)/(√(50)))= 2.357`

And we can find the probability using the normal distribution table and we got:

`P(z<2.357) =0.9908`