Question Type 1: Finding the probability of outcomes for binomial distribution using the GDC Exercises

A factory produces electronic components. Each component has an $80\%$ chance of passing quality control. If $100$ components are tested, find the probability that more than $65$ pass quality control. Use a GDC to compute your answer.

In a large batch of widgets, the defect rate is 20%. From a random sample of 100 widgets, find the probability that between 60 and 75 non-defective widgets are found (inclusive). Use a GDC.

A clinical trial shows each patient has an 80% chance of recovery. If 100 patients are treated, find the probability that at most 70 recover. Compute your answer using a GDC.

Calculate $P\bigl(|X-80|>10\bigr)$ for $X\sim B(100,0.8)$ using a GDC.

Let $X \sim \text{B}(100, 0.8)$.

Find the least integer $k$ such that $P(X \ge k) \le 0.1$.

A telecommunications company defines a call success probability of 0.8. For 100 call attempts, find the probability of at least 80 successful connections. Use a GDC.

Find the smallest integer $k$ such that $P(X<k)\ge0.95$ where $X\sim B(100,0.8)$. Use a GDC to determine $k$.

For $X\sim B(100,0.8)$, find the most probable number of successes (the mode). Use reasoning or a GDC to support your answer.

An online platform estimates an 80% success rate for signup completions. Out of 100 visitors, find the probability fewer than 60 complete signup. Use GDC.

In a study, the probability of success on a new drug is 0.8. In 100 trials, what is the probability exactly 85 patients respond positively? Use a GDC.

A production line has an 80% success rate per item. For a lot of 100, find $P(78 \le X \le 85)$ where $X \sim B(100, 0.8)$ using a GDC.