Questions: Directions: For the following questions, 7-10, write an expression for the probability you are trying to find, as an inequality, such as P(x<3), P(x ≥ 9), etc., in the blank provided. Then shade the area associated with the probability you are trying to find on the graph shown. 7. In a locker room of an older part of school building 24% of the lockers get jammed. If one section of the locker room has 20 lockers, what is the probability that less than 4 will get jammed?

Directions: For the following questions, 7-10, write an expression for the probability you are trying to find, as an inequality, such as P(x<3), P(x ≥ 9), etc., in the blank provided. Then shade the area associated with the probability you are trying to find on the graph shown.
7. In a locker room of an older part of school building 24% of the lockers get jammed. If one section of the locker room has 20 lockers, what is the probability that less than 4 will get jammed?

Transcript text: Directions: For the following questions, $7-10$, write an expression for the probability you are trying to find, as an inequality, such as $P(x<3), P(x \geq 9)$, etc., in the blank provided. Then shade the area associated with the probability you are trying to find on the graph shown. 7. In a locker room of an older part of school building 24\% of the lockers get jammed. If one section of the locker room has 20 lockers, what is the probability that less than 4 will get jammed?

Solution

Solution Steps

Step 1: Define the random variable and distribution

Let X be the number of lockers that get jammed. Since 24% of lockers get jammed and we are considering a section of 20 lockers, X follows a binomial distribution with n=20 and p=0.24. We want to find P(X < 4).

Step 2: Express the probability as an inequality

The probability we are trying to find is P(X < 4), which can also be written as P(X ≤ 3).

Step 3: Calculate the probability

P(X < 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3)

Using the binomial probability formula: P(X=k) = (nCk) * p^k * (1-p)^(n-k)

P(X=0) = (20C0) * (0.24)^0 * (0.76)^20 ≈ 0.0032 P(X=1) = (20C1) * (0.24)^1 * (0.76)^19 ≈ 0.0228 P(X=2) = (20C2) * (0.24)^2 * (0.76)^18 ≈ 0.0759 P(X=3) = (20C3) * (0.24)^3 * (0.76)^17 ≈ 0.1526

P(X < 4) ≈ 0.0032 + 0.0228 + 0.0759 + 0.1526 ≈ 0.2545