Answer:
The confidence interval is
Step-by-step explanation:
From the question we are told that
The sample size is n = 118
The number that gave the correct answer is k = 44
Generally the sample proportion is mathematically represented as

=> 
Generally given that the confidence level is 95% the level of significance is mathematically represented as

=> 
Generally from the normal distribution table the critical value of
is
Generally the margin of error is mathematically represented as

=> 
=> 
Generally 95% confidence interval is mathematically represented as

=>
=>
area=legnth times width
we notice this is a special case
(a+b)(a-b)=a^2-b^2
area=(a+3b)(a-3b)=a^2-9b^2
area=a^2-9b^2
Answer:

And we can solve this using the following z score formula:

And if we use this formula we got:

So we can find this probability equivalently like this:

Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where
and
We select n =100. Since the distribution for X is normal then we know that the distribution for the sample mean
is given by:
We want this probability:

And we can solve this using the following z score formula:

And if we use this formula we got:

So we can find this probability equivalently like this:
