Question

Of my students, 75% report that mathematics is a bit stressful for them. I choose a group of six students and ask them if math is stressful. (Calculate to 3 decimal places)

a) What is that probability that exactly 3 of the students say they are stressed about math?

b) what is the probability that more than 4 students say they are stressed about math?

c) Create a binomial distribution to show the possibilities.

Answer 1

a)
Here, n = 6, p = 0.75, (1 - p) = 0.25 and x = 3
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 3)
P(X = 3) = 6C3 * 0.75^3 * 0.25^3
P(X = 3) = 0.132

b)
We need to calculate P(X >= 5).
P(X >= 5) = (6C5 * 0.75^5 * 0.25^1) + (6C6 * 0.75^6 * 0.25^0)
P(X >= 5) = 0.356 + 0.178
P(X >= 5) = 0.534

c)

x	formula	value
0	6C0 * 0.75^0 * 0.25^6	0
1	6C1 * 0.75^1 * 0.25^5	0.004
2	6C2 * 0.75^2 * 0.25^4	0.033
3	6C3 * 0.75^3 * 0.25^3	0.132
4	6C4 * 0.75^4 * 0.25^2	0.297
5	6C5 * 0.75^5 * 0.25^1	0.356
6	6C6 * 0.75^6 * 0.25^0	0.178