Question

twenty percent of adults in a particular community have at least a bachelors degree. suppose x is a binomial random variable that counts the number of adults with at least a bachelors degree in a random sample of 100 adults from the community. if you are using a calculator with the binompdf and binomcdf commands, which of the following is the most efficient way to calculate the probability that at least 60 adults have a bachelors degree, p(x≥60)?

choose the correct answer below.

a. p(x≥60)=1 - binomcdf(100,0.20,60)
b. p(x≥60)=binomcdf(100,0.20,60)
c. p(x≥60)=1 - binomcdf(100,0.20,59)
d. p(x≥60)=binompdf(100,0.20,60)

Explanation:

Step1: Recall binomcdf function

The binomcdf(n,p,k) gives $P(X\leq k)$ where $n$ is the number of trials, $p$ is the probability of success in a single - trial, and $k$ is the number of successes.

Step2: Find $P(X\geq60)$

We know that $P(X\geq60)=1 - P(X < 60)$. Since $P(X < 60)=P(X\leq59)$ for a discrete binomial random variable, and $P(X\leq59)$ can be calculated using binomcdf with parameters $n = 100$, $p=0.20$, and $k = 59$. So $P(X\geq60)=1 -$ binomcdf$(100,0.20,59)$.

Answer:

C. $P(x\geq60)=1 -$ binomcdf$(100,0.20,59)$