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

If $X\sim B(50,0.6)$, find the expected value $E(X)$ and the variance $\operatorname{Var}(X)$.

In 15 independent transmissions the probability of success is $0.2$. If $X$ is the number of successful transmissions, find $E(X)$ and $\operatorname{Var}(X)$.

Suppose $X\sim B(30,p)$ and $E(X)=18$. Find $p$.

Given $X\sim B(20,p)$ with variance $5$, find $p$.

For $X\sim B(80,0.7)$, compute the expected value and standard deviation.

Let $X\sim B(20,0.3)$. Find $P(X\ge5)$.

For $X \sim B(100,0.8)$, calculate $P(X>65)$.

A lightbulb manufacturer has a defect rate of $8\%$. In a batch of 200 bulbs, let $X$ be the number of nondefective bulbs. Find $P(X\ge190)$.

A student guesses randomly on 15 true/false questions ($p=0.5$). If $X$ is the number correct, find $P(X\ge12)$.

Let $X\sim B(n,p)$ satisfy $E(X)=10$ and $\operatorname{Var}(X)=4$. Find $n$ and $p$.

For $X\sim B(n,p)$, determine $p$ if the mean is twice the variance.

Let $X\sim B(n,p)$ and suppose its standard deviation equals half its mean. Find a relation between $n$ and $p$.