suppose that 70% of all college students love math. in a random sample of 8 college students, let x be the number of students who love math.find p(x=6)
70% of 8 students would be 5.6, so estimate either 5 or 6
A researcher wishes to examine the portion of college students who cheat on exams . A poll of 560 college students showed 27% tried to cheat find the 95% confident interval. Please
To find the probability P(X = 6), where X represents the number of students who love math in a random sample of 8 college students, we can use the binomial probability formula.
The binomial probability formula is given by:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
- n is the total number of trials (sample size)
- k is the number of successful outcomes (students who love math)
- p is the probability of a successful outcome in a single trial
In this case, n = 8 (total number of college students in the random sample), k = 6 (number of students who love math), and p = 0.70 (probability that a college student loves math).
To calculate (n choose k), you can use the combination formula:
(n choose k) = n! / (k! * (n-k)!)
Let's plug in the values and calculate the probability:
P(X = 6) = (8 choose 6) * (0.70)^6 * (1-0.70)^(8-6)
Calculating (8 choose 6):
(8 choose 6) = 8! / (6! * (8-6)!)
= 8! / (6! * 2!)
= (8 * 7 * 6!) / (6! * 2)
= 8 * 7 / 2
= 28
Now, substitute the values into the formula:
P(X = 6) = 28 * (0.70)^6 * (0.30)^(8-6)
= 28 * 0.1176 * 0.09
= 0.27994
Therefore, the probability P(X = 6) is approximately 0.27994, or 27.994%.