Question

There are 40 students in Mr. Jackson’s Math Club. All the students are between the ages of 15 and 18. The table below shows how many students in the club are each age.

Age: 15 16 17 18
Number of students: 9 12 8 11

Part A: Complete this table to show the probability distribution for the club’s age data.

Age (x) 15 16 17 18
Probability (p) 9/40 3/10 1/5 11/40
x(p) 3.375 4.8 3.4 4.95

Answer 1

B. Part B: Mr. Jackson randomly selects one student in the Math Club to be his assistant in an experiment. Use your table from Part A to find what age you expect that student to be (mean, or expected value, of the population).

Mean= 15(9/40)+16(3/10)+17(1/5)+18(11/40)/ 4
3.375+4.8+3.4+4.95=16.525

Answer 2

Part C: Use Parts A and B and the table below to find the variance and standard deviation of the probability distribution.
Age 15 16 17 18
(x-mean) -1.525 -.525 0.475 1.475
(x-mean) 2.325625 .2756 25 .225625 2.175625
(x-mean)2p .52326562 .0826875 .045125 .598296875

Variance= .58140625
Standard deviation= .7625

CONTINUOUS RANDOM VARIABLES

Mr. Jackson will announce the student he selected during today's Math Club meeting. The meeting starts at 11:30 a.m. and ends at noon. The exact time of the announcement will be completely random.

QUESTION: What will be the shape of the density graph for these data? How do you know?