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kotegsom [21]
3 years ago
8

Consider the probability that greater than 99 out of 158 flights will be on-time. Assume the probability that a given flight wil

l be on-time is 64%. Approximate the probability using the normal distribution. Round your answer to four decimal places
Mathematics
1 answer:
Nikitich [7]3 years ago
8 0

Answer:0.1514

Step-by-step explanation:

Let n be the no of flights on time =145

Let  p be the probability that a flight be on time=0.64

Check the condition for normal approximation to the binomial distribution

np\geq 10

92.8\geq 10

Also

n(1-p)\geq 10

52.2\geq 10

Both the conditions satisfied ,so the normal distribution can be used to approximate probability

mean\mu =92.8

Standard deviation\left ( \sigma \right )=\sqrt{np\left ( 1-p\right )}

\sigma =5.779

P\left ( X>99\right )=1-P\left ( x\leqslant 99\right )

P\left ( X>99\right )=1-P\left ( \frac{x-\mu }{\sigma }\leq \frac{99-92.8}{5.779}\right )

P\left ( X>99\right )=1-P\left [ 1.072\right ]

P=1-08485\approx 0.1514

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