Which of the following values is the 25th percentile?lower quartile, median, upper quartile
2 answers:
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Answer:
a) P(x=108)=0.0020
b) P(x≥108)=0.9980
c) P(x<124)=0.7794
d) P(124≤x≤128)=0.1925
Step-by-step explanation:
We know the population proportion, that is p=0.84.
We take a sample of size n=143.
We will use the normal approximation to the binomial distribution to model this problem.
The mean and standard deviation of the normal approximation to the binomial distribution will be:
a) We have to calculate the probability that exactly 108 flights are on time.
As the normal distribution considers the random variable to be continous, we have to apply the continuity correction factor.
In this case, the probability of 108 flights on time can be calculated as P(107.5<x<108.5):
b) Now we have to calculate that at least 108 flights are on time.
As the probability includes 108, the continuity factor will indicates that we calculate P(x>107.5). The z-value for x=107.5 has been already calculated in point a:
c) We have to calculate the probability that fewer than 124 flights are on time. According to the continuity factor, we have to calculate the probability P(x<123.5), as the flight number 124 is not included in the interval.
d) We have to calculate the probability that between 124 and 128 flights, inclusive, are on time.
This interval corresponds to the probability P(123.5<x<128.5)
Answer:
see below
Step-by-step explanation:
The function f(x) is the absolute value function scaled vertically and shifted up. Neither of those transformations affects the interval on which it is increasing. The absolute value function increases for x > 0. (It is neither increasing nor decreasing at x=0.)
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The function g(x) is a parabola that opens downward. Consequently, it is increasing for all values of x to the left of its vertex (or line of symmetry). That line of symmetry can be found as ...
x = -b/(2a) = -(8)/(2·(-1)) = 4
So g(x) is increasing from -∞ to 4, but at x=4 is neither increasing nor decreasing.
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Then the interval on which both functions are increasing is ...
{x > 0} ∩ {x < 4} = {0 < x < 4}
This will be graphed as a line between 0 and 4 with open circles at each end.
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The second attachment shows the two functions so you can see where their slopes are positive.
Answer:
400 square meters
Step-by-step explanation:
We can first solve this problem with each unit representing 1 centimeter, and then scale up at the very end. The shape that we have a parallelogram. The base is 8 cm, and the height is 2 cm. The formula for the area of a parallelogram is just , so the area of the parallelogram is 16 square centimeters. However, now we scale up. Since each centimeter correlates to 5 meters, each little box will correlate to 25 square meters. Therefore,
square meters is our answer