https://file.aiquickdraw.com/mathbot/file/17289231211571h1gp26c.jpg

Let's break down the two problems from the image:

### Problem 1: Pharmaceutical Company Sampling Ibuprofen Tablets
- **Context**: A pharmaceutical company tests ibuprofen tablets from a large shipment by randomly selecting and testing 23 tablets. The batch is accepted if at most 1 tablet is defective. It is given that 11% of the tablets are defective.
- **Objective**: To find the probability that this shipment will be accepted (i.e., the probability that at most 1 tablet is defective out of 23).

#### Solution Approach:
This situation can be modeled using the **binomial distribution**, where:
- \( n = 23 \) (number of trials/tablets),
- \( p = 0.11 \) (probability that a tablet is defective),
- \( k = 0 \) or \( 1 \) (at most 1 defective tablet for acceptance).

The probability mass function for a binomial distribution is given by:
\[
P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}
\]
Where \( X \) represents the number of defective tablets.

We need to calculate the probabilities for \( X = 0 \) and \( X = 1 \), then sum these two probabilities to get the total probability of accepting the batch.

### Problem 2: Tech CEOs and Social Media Use
- **Context**: A CNN story reported that 80% of tech CEOs do not let their children use social media. The goal is to find the probability that, out of 30 randomly selected tech CEOs, at least 25 do not allow their kids to use social media.
- **Objective**: Find \( P(X \geq 25) \), where \( X \) is the number of CEOs who do not allow social media use.

#### Solution Approach:
This also follows a **binomial distribution**, where:
- \( n = 30 \),
- \( p = 0.80 \),
- \( k \geq 25 \).

We need to calculate the cumulative probability for \( X = 25 \), \( X = 26 \), \( X = 27 \), \( X = 28 \), \( X = 29 \), and \( X = 30 \).

Would you like me to perform the detailed calculations for both problems?

A pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. The plan randomly selects and tests 23 tablets, and the shipment is accepted if at most 1 defective tablet is found. What is the probability of accepting the shipment if the defect rate is 11%? Also, a CNN report states that 80% of tech CEOs do not allow their children to use social media. What is the probability that out of 30 randomly selected CEOs, at least 25 do not allow their children to use social media?

Solve two real-world probability problems involving binomial distribution: pharmaceutical sampling for defective tablets and tech CEO restrictions on social media use by their children. Learn how to apply the binomial probability formula to find the likelihood of a shipment being accepted or CEOs restricting social media use.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation