Sixty percent of the students at a particular community college are female.
If 13 students at that community college are selected at random,
find the probability that 5 or 6 students will be female.
Use Appendix Table or Excel function for Binomial distribution.
[Remember from previous test: P(5 or 6) = P(5) + P(6) ]
I don't have your Appendix, nor do I know which Excel function you are talking about, but ..
Prob (female) = 60/100 = 3/5
prob (male) = 2/5
prob (5 of 13 are female) = C(13,5)(3/5)^5 (2/5)^8
= 1287 (.07776)(.0006553) = .06559
do prob(6 of 13 are female) the same way and add up the 2 results.
. The ratio of x to y is 3:1.
a. When x is 9, y is .
Hint: If the answer is a fraction, use the format x/y.
10. The ratio of x to y is 3:1.
a. When x is 9, y is .
Hint: If the answer is a fraction, use the format x/y.
11. b. When x is 3, y is .
Hint: If the answer is a fraction, use the format x/y.
12. c. When x is 1, y is .
Hint: If the answer is a fraction, use the format x/y.
13. In a right triangle, the ratio of side a to side b is 2:1.
a. When side b is 2 inches, side a is ".
14. b. When side b is 2 inches, side c is ".
Hint: Draw a right triangle and label the sides. Use the Pythagorean theorem to find the length of side c to two decimal places.
15. A rectangle has a ratio of L:W = 1:3.
a. Side L = 6 inches, so side W = inches.
16. b. The area of the rectangle is square inches.
17. The ratio of any circle’s radius to its diameter is 1:2.
When a circle has a radius of 2, its diameter is .
Hint: If the answer is a fraction, use the format x/y.
18. When a circle has a radius of 1, its diameter is .
Hint: If the answer is a fraction, use the format x/y.
19. When a circle has a radius of 8, its diameter is .
Hint: If the answer is a fraction, use the format x/y.
20. When a circle has a diameter of 4, its radius is .
To find the probability that 5 or 6 students will be female out of a random selection of 13 students, we can use the binomial distribution. The binomial distribution helps us calculate the probability of obtaining a specific number of successes (in this case, selecting female students) out of a fixed number of trials (in this case, selecting 13 students).
Using the binomial distribution formula, we can calculate the probability of selecting a specific number of female students using the formula:
P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
- P(X=k) is the probability of getting exactly k successes
- C(n, k) is the binomial coefficient, which represents the number of ways to choose k successes from n trials
- p is the probability of success (in this case, the probability of selecting a female student)
- n is the total number of trials (in this case, the total number of students selected)
Now, let's calculate the probability using this formula:
First, let's find the probability of selecting 5 female students:
P(X=5) = C(13, 5) * (0.6)^5 * (1-0.6)^(13-5)
Next, let's find the probability of selecting 6 female students:
P(X=6) = C(13, 6) * (0.6)^6 * (1-0.6)^(13-6)
Finally, we can calculate the probability of getting 5 or 6 female students by summing up the individual probabilities:
P(5 or 6) = P(5) + P(6)
To find the values of C(n, k), we can utilize either an appendix table or an Excel function for binomial distribution. The "BINOM.DIST" function in Excel can be used to calculate this probability.