Respuesta :
Answer:
[tex] z =\frac{26-25}{\frac{3}{\sqrt{50}}}= 2.357[/tex]
And we can find the probability using the normal distribution table and we got:
[tex] P(z<2.357) =0.9908[/tex]
Step-by-step explanation:
Let X the random variable of interest and we can find the parameters:
[tex] \mu =25, \sigma= 3[/tex]
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:
[tex] \bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
We want to find the following probability:
[tex] P(\bar X <26)[/tex]
And we can use the z score formula given by:
[tex] z =\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And replacing we got:
[tex] z =\frac{26-25}{\frac{3}{\sqrt{50}}}= 2.357[/tex]
And we can find the probability using the normal distribution table and we got:
[tex] P(z<2.357) =0.9908[/tex]
