Suppose that 92% of all SFSU students own a cell phone. Find the probability that 7 out of 10 random selected SFSU students own a cell phone
To find the probability that 7 out of 10 randomly selected SFSU students own a cell phone, we can use the binomial probability formula.
The probability of a success (owning a cell phone) is given as 92% or 0.92. Let's call this value p. The probability of a failure (not owning a cell phone) is given as 100% - 92% = 8% or 0.08. Let's call this value q.
The binomial probability formula is:
P(X = k) = (n C k) * p^k * q^(n-k)
In this formula:
- P(X = k) represents the probability of getting exactly k successes out of n trials.
- (n C k) represents binomial coefficient, which is the number of ways to choose k items from a set of n items. It can be calculated as n! / (k! * (n-k)!)
- p^k represents the probability of getting k successes.
- q^(n-k) represents the probability of getting (n - k) failures.
In this case, we want to find the probability of getting exactly 7 successes (k = 7) out of 10 trials (n = 10).
P(X = 7) = (10 C 7) * (0.92)^7 * (0.08)^(10-7)
Applying the binomial coefficient:
(10 C 7) = 10! / (7! * (10-7)!) = 10! / (7! * 3!) = (10 * 9 * 8) / (3 * 2 * 1) = 120
Plugging in the values into the formula:
P(X = 7) = 120 * (0.92)^7 * (0.08)^(10-7)
Now, just calculate this expression to find the probability that 7 out of 10 randomly selected SFSU students own a cell phone.