Question

. A study was conducted to determine success rates of students enrolled in the Statistics courses offered at South Plains College for the fall semester of 2015. A random sample of 14 students was taken, and we recorded each student’s age, final average, gender, # hours worked per week, race, and the attendance record (# of classes not attended this semester). Use the results from the following table to answer all parts of #2.

Age	Final Average	Gender	# Hrs worked/wk	Race	Attendance
21	80	F	25	1	1
18	50	M	35	1	6
18	72	M	40	2	2
19	95	F	25	2	0
43	90	M	40	1	0
24	66	M	0	1	4
25	89	M	20	3	1
50	84	F	50	1	0
18	76	F	32	2	1
17	81	F	15	3	0
20	44	F	0	2	7
21	70	F	30	1	3
26	79	F	40	1	0
20	82	F	20	2	1

1. For the age variable, describe the distribution (in terms of symmetry versus skewness)

2. If 4 students are randomly selected, what is the probability that all will be females? (3 pts)

3. We want to estimate the percentage of students next semester who earned a final average of 90 or above. How many students must we survey next semester, if we want our proportion estimate to be within 3 percentage points at a 95% level of confidence? (2 pts)

Answer 1

(1) If we make a histogram of the "age" variable, we see that the data are positively skewed and not at all symmetric. Also, if we calculate the skewness, we get the value to be 1.626. The skewness value being greater than 0 indicates positive skewness. Hence, its distribution is also positively skewed.
(2) There are 5 males and 9 females here. Hence, the probability that all 4 will be females are = = 0.1259.