Female students in the spring 2013 class survey had heights that were approximately Normally distributed with a mean of 64.86 inches and a standard deviation of 3.25. Suppose we took a sample of 25 female students from the population of all the students who took the survey. What is the probability that the mean height of the 25 female students would be between 63.5 and 65.1 inches?

Question

just_one_last_goodbye · Answer

Need help? :D

anonymous · Answer

yes

just_one_last_goodbye · Answer

Go ahead @AlexandervonHumboldt2 ^_^

anonymous · Answer

Female students in the spring 2013 class survey had heights that were approximately Normally distributed with a mean of 64.86 inches and a standard deviation of 3.25. Suppose we took a sample of 25 female students from the population of all the students who took the survey. What is the probability that the mean height of the 25 female students would be between 63.5 and 65.1 inches?

alexandervonhumboldt2 · Answer

@dan815   @ganeshie8   @Hero   


@just_one_last_goodbye   lol i don't really understand the question :(

anonymous · Answer

Probs and Stats

math&ing001 · Answer

The sample of 25 female student is Normally distributed (since the population it was taken from is normally distributed), so it will have the same mean 64.86 inches, and the standard deviation $\sigma = \frac{ 3.25 }{ \sqrt{25} }=0.65$.

Now we find the z scores for the means 63.5 and 65.1 that we'll use to find the probability.
$$z_{1}=\frac{ x-mean }{ \sigma }=\frac{ 63.5-64.86 }{ 0.65 }=-2.09$$$$z_{2}=\frac{ 65.1-64.86 }{ 0.65 }=0.36$$
You can get the probability P(-2.09<z<0.36) using the Normal distribution table.