A brand name has 50% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 6 randomly selected consumers.
How would you do the binomial probability formula can be used to find the simple binomial probabilities for n = 6 and p = 0.5
The formula is given below but I am not sure how to write it to figure out the outcomes for P(0) P(2) P(3) P(4), The formula is P(x) = n!/(n - x)!x! * px * qn –x for x = 0, 1, 2, . . .n
To use the binomial probability formula to find the probabilities for P(0), P(2), P(3), and P(4) with n = 6 and p = 0.5, you can follow these steps:
1. Substitute the values of n and p into the formula: P(x) = n! / ((n - x)! * x!) * p^x * (1 - p)^(n - x)
2. Calculate the outcomes for each probability:
For P(0):
x = 0
P(0) = 6! / ((6 - 0)! * 0!) * 0.5^0 * (1 - 0.5)^(6 - 0) = 1 * 1 * 0.5^0 * 0.5^6 = 0.5^6 = 0.015625
For P(2):
x = 2
P(2) = 6! / ((6 - 2)! * 2!) * 0.5^2 * (1 - 0.5)^(6 - 2) = 6! / (4! * 2!) * 0.5^2 * 0.5^4 = 0.9
For P(3):
x = 3
P(3) = 6! / ((6 - 3)! * 3!) * 0.5^3 * (1 - 0.5)^(6 - 3) = 6! / (3! * 3!) * 0.5^3 * 0.5^3 = 0.3125
For P(4):
x = 4
P(4) = 6! / ((6 - 4)! * 4!) * 0.5^4 * (1 - 0.5)^(6 - 4) = 6! / (2! * 4!) * 0.5^4 * 0.5^2 = 0.234375
Therefore, the outcomes for P(0), P(2), P(3), and P(4) with n = 6 and p = 0.5 are 0.015625, 0.234375, 0.3125, and 0.234375, respectively.