Answer:
n = 66.564
Step-by-step explanation:
- Because the population is unknown, we will apply the following formula to find the sample size:

Where:
z = confidence level score.
S = standard deviation.
E = error range.
2. We will find each of these three data and replace them in the formula.
"z" theoretically is a value that measures how many standard deviations an element has to the mean. For each confidence level there is an associated z value. In the question, this level is 99%, which is equivalent to a z value of 2.58. To find this figure it is not necessary to follow any mathematical procedure, it is enough to make use of a z-score table, which shows the values for any confidence interval.
The standard deviation is already provided by the question, it is S = 100.
Finally, "E" is the acceptable limit of sampling error. In the example, we can find this data. Let us note that in the end it says that the director wishes to estimate the mean number of admissions to within 1 admission, this means that she is willing to tolerate a miscalculation of just 1 admission.
Once this data is identified, we replace in the formula:

3. The corresponding mathematical operations are developed:


n= 66.564
Answer: Our required probability is 0.1695.
Step-by-step explanation:
Since we have given that
Number of male applicants = 4200
Number of female applicants = 3800
So, total number of applicants = 4200+3800 = 8000
Probability of male entered and subsequently enrolled is given by

Probability of female entered and subsequently enrolled is given by

Number of male entered and subsequently enrolled is given by

Number of female entered and subsequently enrolled is given by

So, Probability that a student who applied for admission will be accepted by the university and subsequently will enroll is given by

Hence, our required probability is 0.1695.
Answer: Line R and Line P are perpendicular because they intersect at a point and create a pair of equal angles.
Step-by-step explanation: