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laiz [17]
3 years ago
7

Flight 202's arrival time is normally distributed with a mean arrival time of 6:30 p.m. and a standard deviation of 15 minutes.

Use the eight-part symmetry of the area under a normal curve to find the probability that a randomly chosen arrival time is after 7:15 p.m.
The probability is__
Mathematics
1 answer:
natta225 [31]3 years ago
3 0

Answer:

The probability is 0.0015

Step-by-step explanation:

We know that the mean \mu is:

\mu=6:30\ p.m

The standard deviation \sigma is:

\sigma=0:15\ minutes

The Z-score is:

Z=\frac{x-\mu}{\sigma}

We seek to find

P(x>7:15\ p.m.)

The Z-score is:

Z=\frac{x-\mu}{\sigma}

Z=\frac{7:15-6:30}{0:15}

Z=\frac{0:45}{0:15}

Z=3

The score of Z = 3 means that 7:15 p.m. is 3 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the conficion of 3 deviations from the mean has percentage of 0.15%

So

P(x>7:15\ p.m.)=P(Z>3)=0.0015

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