Question

1. A university found that 10% of students withdraw from a math course. Assume 25 students are enrolled.
   1. Write the prob. distribution function with the specific parameters for this problem

1. 2. Compute by hand (can use calculator but show some work) the pro that exactly 2 withdraw.
2. 3. Compute by hand (can use calculator but show some work) the prob. that exactly 5 withdraw.
3. 4. Construct the probability distribution table of class withdrawals in Excel. This is a table of x and f(x). Generate one column for the number of x successes with numbers 0 to 25 in each row. Generate a second column with the probability f(x) of each success using the Excel function =BINOM.DIST(x, n, p, FALSE) in each row. Attach the table
4. 5. What is the probability that 5 or less will withdraw?

Answer 1

Note:

Hey there! Thank you for the question. As you have posted several subparts, as per our policy, we have solved the first 4 subparts for you.

a.

There are n = 25 students enrolled. Out of these, 10% withdraw from a math course. Thus, the probability of withdrawal is, p = 0.10. It can be assumed that the students withdraw independently.

Hence, the random variable (say, X) representing the number of students who withdraw among the 25, is a binomially distributed random variable.

If X ~ Binomial (n, p), then the probability mass function of X is:

In this case, X has a binomial distribution with parameters n = 25, p = 0.10. Note that, q = 1 – p = 0.90. Thus, X ~ Binomial (25, 0.10). The probability distribution function is:

b.

The probability that exactly 2 students withdraw is, P (X = 2) = p (2), calculated below:

Thus, the probability that exactly 2 students withdraw is 0.2659.

c.

The probability that exactly 5 students withdraw is, P (X = 5) = p (5), calculated below:

Thus, the probability that exactly 2 students withdraw is 0.0646.

d.

By following the instructions given in Part d, the following table is obtained. We have taken the probabilities to 4 decimal places.

x	f (x)
0	0.0718
1	0.1994
2	0.2659
3	0.2265
4	0.1384
5	0.0646
6	0.0239
7	0.0072
8	0.0018
9	0.0004
10	0.0001
11	0.0000
12	0.0000
13	0.0000
14	0.0000
15	0.0000
16	0.0000
17	0.0000
18	0.0000
19	0.0000
20	0.0000
21	0.0000
22	0.0000
23	0.0000
24	0.0000
25	0.0000
Total	1