Question

**(Can this be done on a Ti-84?)** A certain flight
arrives on time 83 percent of the time. Suppose140 flights are
randomly selected. Use the normal approximation to the binomial to
approximate the probability that

?(a) exactly 109 flights are on time.

?(b) at least 109 flights are on time.

?(c) fewer than 114 flights are on time.

?(d) between 114 and 128 inclusive are on time.

Answer #1

**Solution:-**

**p = 0.83**

n = 140

Mean = n × p

Mean = 140 × 0.83

**Mean = 116.2**

**a) The probability that exactly 109 flights are on time
is 0.021.**

x = 109

By applying normal distruibution:-

z = - 1.162

**P(z = - 1.162) = 0.021**

**b) The probability that at least 109 flights are on time
is 0.8776.**

x = 109

By applying normal distruibution:-

z = - 1.162

P(z > -1.162) = 0.8776

**c) The probability that a fewer than 114 flights are on
time is 0.3101.**

x = 114

By applying normal distruibution:-

z = - 0.495

P(z < - 0.495) = 0.3101

**d) The probability that between 114 and 128 inclusive
are on time is 0.6857.**

x_{1} = 114

x_{2} = 128

By applying normal distruibution:-

z_{1} = - 0.495

z_{2} = 2.65

P(- 0.495 < z < 2.65) = P(z > - 0.495) - P(z > 2.65)

P(- 0.495 < z < 2.65) = 0.6897 - 0.004

P(- 0.495 < z < 2.65) = **0.6857**

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