Decide whether you can use the nomal distribution to approximate the binomial di
ID: 3065781 • Letter: D
Question
Decide whether you can use the nomal distribution to approximate the binomial distributon. If you can, use the normal distribution to approximate the indicated probabilities and skeich their graphs If you cannot, explain why and use the binomial distribution to find th indicated probabilities Five percant of workers in a city use public transportation to get to work. You randomily select 265 workers and ask them if they use public transportation to get to work. Complate parts (a) through (d) Can the normal distribution be used to approximatc the binomial distnioution? O A. No, because nq s. O B. Yes, because both np 5 and nq 2.5 O C. No, because npExplanation / Answer
Option - b) Because np > 5 and nq > 5
mean = n * p = 265 * 0.05 = 13.25
standard deviation = sqrt(n * p * (1 - p)) = sqrt(265 * 0.05 * 0.95) = 3.55
a) P(X = 17)
= P(-16.5 < X < 17.5)
= P((16.5 - mean)/sd < (x - mean)/sd < (17.5 - mean)/sd)
= P((16.5 - 13.25)/3.55 < Z < (17.5 - 13.25)/3.55)
= P(0.92 < Z < 1.20)
= P(Z < 1.20) - P(Z < 0.92)
= 0.8849 - 0.8212
= 0.0637
Option - C is correct graph
b) P(X > 7)
= P(X > 7.5)
= P((x - mean)/sd > (7.5 - mean)/sd)
= P(Z > (7.5 - 13.25)/3.55)
= P(Z > -1.62)
= 1 - P(Z < -1.62)
= 1 - 0.0526
= 0.9474
Option - B is correct graph.
c) P(X < 17)
= P(X < 17.5)
= P((x - mean)/sd < (17.5 - mean)/sd))
= P(z < (17.5 - 13.25)/3.55)
= P(Z < 1.20)
= 0.8849
Option - C is correct graph.
d) mean = 548 * 0.05 = 27.4
sd = sqrt(548 * 0.05 * 0.95) = 5.1
Probability of not getting discount = P(X < 30)
= P((X - mean)/sd < (30.5 - mean)/sd)
= P(Z < (30.5 - 27.4)/5.1)
= P(Z < 0.61)
= 0.7291
Option - B is correct graph.
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