Question

in a large metropolitan area, past records revealed that 30 percent of all the high school graduates go to college. From 10 graduates selected at random what is the probability that: More than 5 and less than 9 will go to college

Answer 1

The question represents a binomial distribution.

The binomial probability formula is calculated using the formula:

`P(X)=^nC_Xp^X(1-p)^(n-X)`

where

P = binomial probability

X = number of times for a specific outcome within n trials

n C x = number of combinations

p = probability of success on a single trial

n = number of trials

From the question, we have the following parameters:

`\begin{gathered} p=30\%=0.3 \\ n=10 \end{gathered}`

We are to evaluate the probability that more than 5 and less than 9, hence:

`P(5<strong>At X = 6:</strong>[tex]\begin{gathered} P(6)=^(10)C_6\cdot0.3^6\cdot(1-0.3)^(10-6) \\ P(6)=0.0368 \end{gathered}`

At X = 7:

`P(7)=0.0090`

At X = 8:

`P(8)=0.0014`

Therefore, the probability will be:

[tex]P(5The probability is 0.0472.