Binomial Scenario Worksheet
Binomial Scenario Challenge
Name:
Date:
Instructions:
Solve each real-world scenario using the binomial distribution X ~ B(n, p). For each problem, identify your parameters and show your formula setup. You may use a calculator for final probability values. Match your answers to the letter key to determine the color for your coloring sheet. 🎨
Problem 1: Blue
A local printing press finds that 22% of books in a large run have minor ink smudges. In a random batch of 30 books, what is the probability that at most 12 books have smudges?
n = _______ p = _______
Ans: ________ (Key: ____)
Problem 2: Lime Green
A gardener plants 47 heirloom seeds. Historical data suggests only 2/7 of these seeds will sprout in the first week. What is the probability that no more than 13 seeds sprout?
n = _______ p = _______
Ans: ________ (Key: ____)
Problem 3: Brown
To decide who starts a picnic game, a group flips a fair coin 18 times. Let X be the number of "Tails" obtained. Calculate the variance for the number of tails in this set of flips.
n = _______ p = _______
Ans: ________ (Key: ____)
Problem 4: Orange
A specific coffee shop has a 50% chance of being crowded at 8:00 AM on any given weekday. Over the next five weekdays, what is the probability the shop is crowded exactly three times?
n = _______ p = _______
Ans: ________ (Key: ____)
Problem 5: Goldenrod
A board game spinner is divided into four equal sections. If you spin it 6 times, what is the probability that it lands on the "Bonus" section exactly twice?
n = _______ p = _______
Ans: ________ (Key: ____)
Problem 6: Purple
A school finds that 12% of its student lockers occasionally get stuck. If a new bank of 40 lockers is installed, what is the probability that no more than 5 of them will get stuck?
n = _______ p = _______
Ans: ________ (Key: ____)
Problem 7: Green
A basketball player successfully makes free throws 2/3 of the time. If she attempts 98 free throws this season, what is the probability that she makes at least 70 of them?
n = _______ p = _______
Ans: ________ (Key: ____)
Problem 8: Red
A biologist is studying butterflies where the chance of a caterpillar being female is 50%. In a cluster of 5 eggs, what is the expected number of female butterflies?
n = _______ p = _______
Ans: ________ (Key: ____)
Problem 9: Light Yellow
When Kyle doesn't study for his tests, he has a 45% chance of passing. If Kyle skips studying for 15 tests this year, what is the probability he passes at least 3 of them?
n = _______ p = _______
Ans: ________ (Key: ____)
Problem 10: Red Orange
A biased die is thrown 60 times and a 'Four' is rolled 12 times. If the die is thrown 14 more times, what is the expected number of 'Fours' for these additional throws?
n = _______ p = _______
Ans: ________ (Key: ____)
Problem 11: Lilac
A birdwatcher notes that 37.5% (3/8) of the birds in their yard are sparrows. If they see 10 birds today, what is the probability that more than 3 of them are sparrows?
n = _______ p = _______
Ans: ________ (Key: ____)
Problem 12: White
A survey of park visitors shows that 60% of people prefer tea over coffee. If a group of 10 people is surveyed, what is the expected number of people who prefer tea?
n = _______ p = _______
Ans: ________ (Key: ____)
A: 0.297
B: 0.553
C: 4.5
D: 0.654
E: 6.00
F: 0.313
G: 0.993
H: 2.8
I: 2.5
J: 0.989
K: 0.518
L: 0.187
