Statistical Distribution
\(\(P(X=r)=\begin{pmatrix}n \\r\end{pmatrix}p^r(1-p)^{n-r}\)\)
Where:
- \(X\) is the description of the random variable
- \(p\) is the probability
- \(n\) is the number of trials
Using \(X\sim B(20,0.4)\)
1. \(P(X\leq7)=0.4159\)
2. \(P(X<6)=P(X\leq5)=0.1256\)
3. \(P(X\geq15)=1-P(X\leq14)=0.0016\)
4. \(P(6<X\leq10)=P(X\leq10)-P(X\leq6)\)
5. \(P(X>20)=1-P(X\leq20)\)
6. \(P(20<X<30)=P(X\leq29)-P(X\leq20)\)
a. Prob that spinner lands on red is 0.3
Jane does 12 spins
Find the probability she gets at least 5 reds. = 0.276
b. Probability of winning a prize is < 0.05. Each member of the class will have 12 spins.
How many reds are needed to win? - 7 reds (gives probability of 0.0386)
20 exams at the end of the year
pass rate for each exam is 0.45.
exam administrators want a certain number of exams to be passed to continue at school.
How many test should students have to pass for the pass rate to be 90%.
Lower bound: 6
Upper bound: 20
Numtrial: 20
Prob: 0.45
=
0.94 (works)
Lower bound: 7
Upper bound: 20
Numtrial: 20
Prob: 0.45
=
0.87 (doesnt work
a. 13/50
b. 28/50
a. k=1
b. r=9
c. 0.98
- Binomial Distribution
- 0.1503
- s= (if s=7, then prob=0.0106 (too big))
- 0.28 (lower = 0, upper = 1)
- 0.1036 (lower = 5, upper=50)
- d=5 because 5-50 prob is 0.10 (and when d=6, prob = 0.0377 which is when the factory stops so it needs to be GREATER than 5)