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NARA [144]
2 years ago
6

Delta Airlines quotes a flight time of 2 hours for its flights from Cincinnati to Tampa, meaning that an on-time flight would ar

rive in 2 hours. Suppose we believe that actual flight times are uniformly distributed between 1 hour 50min minutes and 135 minutes.a. Show the graph of the probability density function for flight time.b. What is the probability that the flight will be no more than 5 minutes late?c. What is the probability that the flight will be more than 10 minutes late?d. What is the expected flight time?

Mathematics
1 answer:
ddd [48]2 years ago
6 0

Answer:

a) Attached

b) P=0.60

c) P=0.80

d) The expected flight time is E(t)=122.5

Step-by-step explanation:

The distribution is uniform between 1 hour and 50 minutes (110 min) and 135 min.

The height of the probability function will be:

h=\frac{1}{Max-Min}=\frac{1}{135-110} =\frac{1}{25}

Then the probability distribution can be defined as:

f(t)=\frac{1}{25}=0.04 \,\,\,\,\\\\t\in[110,135]

b) No more than 5 minutes late means the flight time is 125 or less.

The probability of having a flight time of 125 or less is P=0.60:

F(T

c) More than 10 minutes late means 130 minutes or more

The probability of having a flight time of 130 or more is P=0.80:

F(T>t)=1-0.04(t-110)\\\\F(T>130)=1-0.04*(130-110)=1-0.04*20=1-0.8=0.2

d) The expected flight time is E(t)=122.5

E(t)=\frac{1}{2}(max+min)= \frac{1}{2}(135+110)=\frac{1}{2}*245=122.5

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Answer:

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Step-by-step explanation:

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4 0
3 years ago
Simplify the expression. (3.5x - 5) + (7.2x + 10)
Andru [333]

Answer: 10.7x + 5

Step-by-step explanation:

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8 0
2 years ago
The mean yearly rainfall in Sydney, Australia, is about 134 mm and the standard deviation is about 66 mm ("Annual maximums of,"
svetlana [45]

Answer:

At least 202.44 mm in the top 15%.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 134, \sigma = 66

How many yearly mm of rainfall would there be in the top 15%?

At least X mm.

X is the 100-15 = 85th percentile, which is X when Z has a pvalue of 0.85. So X when Z = 1.037.

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

1.037 = \frac{X - 134}{66}

X - 134 = 66*1.037

X = 202.44

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5 0
3 years ago
Find the value of k given that the line through (k,2) and (7,0) is perpendicular to the line y=x-28/5
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slope = (y2 - y1) / (x2 - x1)
(k,2)....x1 = k and y1 = 2
(7,0)...x2 = 7 and y2 = 0
sub
slope = (0 - 2) / (7 - k)
slope = -2 / ?......now if we want the slope to be -1..that means the number where the question mark is has to be 2....for that to happen, k has to be 5...because 7 - 5 = 2.

so ur answer is : k = 5
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3 years ago
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babymother [125]

Answer:

First one is True, Second is false

Step-by-step explanation:

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7 0
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