Question

32) According to American Airlines, Flight 215 from Orlando to Los Angeles is on time 90% of the time. Randomly select 150 flights and use the normal approximation to the binomial to approximate the probability that at least 125 flights are on time 33) of all 3-to 5-year-old children, 56% are enrolled in school. If a sample of 500 such children is randomly selected, use the normal approximation to the binomial to approximate the probability that at most 200 will be enrolled in school.

Answer 1

#32.
p = 0.9 and n = 215
mean = np = 215 * 0.9 = 193.5
sd = sqrt(215*0.9*0.1) = 4.3989

P(X >= 125)
= P(X > 124.5)
= P(z > (124.5 - 193.5)/4.3989)
= P(z > -15.69)
= 1

#33.
p = 0.56 and n = 500
mean = np = 500 * 0.56 = 280
sd = sqrt(500*0.56*0.44) = 11.0995

P(X <= 200)
= P(X < 199.5)
= P(z < (199.5 - 280)/11.0995)
= P(z < -7.25)
= 0