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 254 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 binomialdistribution?
A.
Yes, because both
np greater than or equals?5
and
nq greater than or equals?5.
B.
No, because
nq less than<5.
C.
No, because
np less than<5.
(a) Find the probability that exactly
1919
workers will say yes.
What is the indicated probability?
nothing
(Round to four decimal places as needed.)
Sketch the graph of the normal distribution with the indicatedprobability shaded.
(b) Find the probability that at least
77
workers will say yes.
What is the indicated probability?
nothing
(Round to four decimal places as needed.)
Sketch the graph of the normal distribution with the indicatedprobability shaded.
A.
1317x
mu equals 12.7?=12.7
x y graph
B.
1317x
mu equals 12.7?=12.7
x y graph
C.
1317x
mu equals 12.7?=12.7
x y graph
D.
The normal distribution cannot be used to approximate thebinomial distribution.
(c) Find the probability that fewer than
1919
workers will say yes.
What is the indicated probability?
nothing
(Round to four decimal places as needed.)
Sketch the graph of the normal distribution with the indicatedprobability shaded.
A.
13119x
mu equals 12.7?=12.7
x y graph
B.
13119x
mu equals 12.7?=12.7
x y graph
C.
13119x
mu equals 12.7?=12.7
x y graph
D.
The normal distribution cannot be used to approximate thebinomial distribution.
(d) A transit authority offers discount rates to companies thathave at least
3030
employees who use public transportation to get to work. Thereare
499499
employees in a company. What is the probability that the companywill not get the discount?
Can the normal distribution be used to approximate the binomialdistribution?
A.
No, because
npless than<5.
B.
Yes, because both
npgreater than or equals?5
and
nqgreater than or equals?5.
C.
No, because
nqless than<5.
What is the probability that the company will not get thediscount?
nothing
(Round to four decimal places as needed.)
Sketch the graph of the normal distribution with the indicatedprobability shaded.
