Decide whether you can use the normal distribution toapproximate the binomial distribution. If you​ can, use the normaldistribution to approximate the indicated probabilities and sketchtheir graphs. If you​ cannot, explain why and use the binomialdistribution to find the indicated probabilities. Five percent ofworkers in a city use public transportation to get to work. Yourandomly select 269 workers and ask them if they use publictransportation to get to work.
(Complete parts A through D)
Can the normal distribution be used to approximate the binomial​distribution?
a.​Yes, because both np ≥ 5 and nq ≥ 5.
b.​No, because np < 5.
c.​No, because nq <5.
A) ​- Find the probability that exactly20 workers will say yes.
What is the indicated​ probability? (____) Round to fourdecimal places as​ needed.
Sketch the graph of the normal distribution with the indicatedprobability shaded.
B) ​- Find the probability that at least7 workers will say yes.
What is the indicated​ probability? (____) Round to fourdecimal places as​ needed.
Sketch the graph of the normal distribution with the indicatedprobability shaded.
C) - Find the probability that fewer than20 workers will say yes.
What is the indicated​ probability? (____) Round to fourdecimal places as​ needed.
Sketch the graph of the normal distribution with the indicatedprobability shaded.
D) - A transit authority offers discount ratesto companies that have at least 30 employees whouse public transportation to get to work. There are452 employees in a company. What is theprobability that the company will not get the​ discount?
Can the normal distribution be used to approximate the binomial​distribution?
a.​ No, because nq < 5.
b.​ No, because np < 5.
c.​ Yes, because both np ≥ 5 and nq ≥ 5.
What is the probability that the company will not get the​discount? (____) Round to four decimal places as​needed.
Sketch the graph of the normal distribution with the indicatedprobability shaded.
