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Math (Stats) Question. Please help!?
A certain flight arrives on time 88% of the time. Suppose 142 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that:
A: exactly 123 flights are on time
B: at least 123 flights are on time
C: fewer than 132 flights are on time
D: between 132 and 134, inclusive are on time.
Also, is there a way to solve this on a ti-83 calculator? Thank you very much!!!!!!!
1 Answer
- Julius NLv 71 decade agoFavorite Answer
n = 142; p = 0.88; q = 0.12; x = 1
μ = (n p) = 124.96; σ² = ( n p q ) = 14.9952; σ = √( n p q ) = 3.8724
z = ( x - μ ) / σ
A: P (122.5 < x < 123.5) = P (-0.6353 < z < -0.377) = 0.0904
B: P (x > 122.5) = P (z > -0.6353) = 0.7374
C: P ( x < 131.5) = P ( z < 1.6889 ) = 0.9544
D: P (131.5 < x < 134.5) = P (1.6889 < z < 2.4636) = 0.0387