Respuesta :
Answer:
[tex]P(X<68)=P(\frac{X-\mu}{\sigma}<\frac{68-\mu}{\sigma})=P(Z<\frac{68-69.1}{4.0})=P(z<-0.275)[/tex]
And we can use the normal standard distribution table or excel to find the probability of interest:
[tex]P(z<-0.275)=0.392[/tex]
So then we can conclude that the probability that a study participant has a height less than 68 is approximately 0.392 or 39.2%
Step-by-step explanation:
We can define X as the random variable that represent the heights of a population desired, and for this case we know the distribution for X is given by:
[tex]X \sim N(69.1,4.0)[/tex]
Where [tex]\mu=69.1[/tex] and [tex]\sigma=4.0[/tex]
We want to find the following probability:
[tex]P(X<68)[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this z score formula we have this:
[tex]P(X<68)=P(\frac{X-\mu}{\sigma}<\frac{68-\mu}{\sigma})=P(Z<\frac{68-69.1}{4.0})=P(z<-0.275)[/tex]
And we can use the normal standard distribution table or excel to find the probability of interest:
[tex]P(z<-0.275)=0.392[/tex]
So then we can conclude that the probability that a study participant has a height less than 68 is approximately 0.392 or 39.2%
