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katovenus [111]
3 years ago
7

When Harper commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 24 minutes and a

standard deviation of 3 minutes. Using the empirical rule, determine the interval that represents the middle 95% of her commute times.
Mathematics
1 answer:
Korvikt [17]3 years ago
7 0

Answer:

\mu -2\sigma = 24-2*3= 18

\mu -2\sigma = 24+2*3= 30

So then we can conclude that we expect the middle 95% of the values within 18 and 30 minutes for this case

Step-by-step explanation:

For this case we can define the random variable X as the amount of time it takes her to arrive to work and we know that the distribution for X is given by:

X \sim N(\mu = 24, \sigma =3)

And we want to use the empirical rule to estimate the middle 95% of her commute times. And the empirical rule states that we have 68% of the values within one deviation from the mean, 95% of the values within two deviations from the mean and 99.7 % of the values within 3 deviations from the mean. And we can find the limits on this way:

\mu -2\sigma = 24-2*3= 18

\mu -2\sigma = 24+2*3= 30

So then we can conclude that we expect the middle 95% of the values within 18 and 30 minutes for this case

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Answer:

An airline estimates that 94% of people booked on their flights actually show up. If the airline books 77 people on the flight for which the maximum number is 75, what is the probability that the number of people who show up will exceed the capacity of the plane?

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---

P(76 <= x <= 77) = 1-P(0 <=x <= 75) = 1 - binomcdf(77,0.94,75) = 0.0504

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Cheers,

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Answer:

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