The passing rate for the boards is 34%. If 70 people take the boards, the probability that 30 of them will pass the exam is?
Try the binomial probability function:
P(x) = (nCx)(p^x)[q^(n-x)]
x = 70
n = 30
p = .34
q = 1 - p = 1 - .34 = .66
Substitute the values and go from there.
An easier way would be to use a binomial probability table with the values stated above.
I hope this will help.
Correction:
x = 30
n = 70
The other values stay the same.
Sorry for any confusion.
To find the probability that exactly 30 people will pass the exam out of 70 who take the boards, we can use the binomial probability formula.
The binomial probability formula can be represented as:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
- P(X = k) is the probability of obtaining exactly k successes (30 people passing the exam).
- n is the number of trials (70 people taking the boards).
- k is the number of successful trials (30 people passing the exam).
- C(n, k) is the number of ways to choose k successes from n trials, also known as binomial coefficient.
- p is the probability of success in each trial (passing rate = 34% = 0.34).
- (1 - p) is the probability of failure in each trial (1 - passing rate).
Let's calculate the probability using the given values:
P(X = 30) = C(70, 30) * (0.34)^30 * (1 - 0.34)^(70 - 30)
To calculate the binomial coefficient C(70, 30), we can use the formula:
C(n, k) = n! / (k! * (n - k)!)
Now, let's calculate the probability step by step.
Step 1: Calculate the binomial coefficient, C(70, 30):
C(70, 30) = 70! / (30! * (70 - 30)!)
Step 2: Calculate the values of p, (0.34)^30, and (1 - 0.34)^(70 - 30).
Step 3: Plug in the values into the binomial probability formula:
P(X = 30) = C(70, 30) * (0.34)^30 * (1 - 0.34)^(70 - 30)
By evaluating this expression, you will find the probability that exactly 30 people will pass the exam out of 70 who take the boards.