Sixty percent of all vehicles examined at a certain emissions inspection station pass the inspection. Assuming that successive v
ehicles pass or fail independently of one another, calculate the following probabilities. (Enter your answers to three decimal places.)(a)P(all of the next three vehicles inspected pass)
(b)P(at least one of the next three inspected fails)
(c)P(exactly one of the next three inspected passes)
(d)P(at most one of the next three vehicles inspected passes)
(e) Given that at least one of the next three vehicles passes inspection, what is the probability that all three pass (a conditional probability)?
(b)P(at least one of the next three inspected fails)
(c)P(exactly one of the next three inspected passes)
(d)P(at most one of the next three vehicles inspected passes)
(e) Given that at least one of the next three vehicles passes inspection, what is the probability that all three pass (a conditional probability)?
1 answer:
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Solution:
Given that
G being the midpoint of FH implies
Additionally, we have
Hence, we can express
Therefore,
Response:
PQ's slope is 0
MN's slope equals infinity
The lines PQ and MN are perpendicular to one another
Detailed explanation:
For two points in the coordinate plane, denoted as (x1, y1) and (x2, y2), the slope is determined as follows:
If a line has a slope of zero, it runs parallel to the X-axis and stands perpendicular to the Y-axis
If a line's slope is infinite, it is parallel to the Y-axis and perpendicular to the X-axis
Moreover, it is established that X and Y are perpendicular to each other.
As PQ's slope is zero, it runs parallel to the X-axis and perpendicular to the Y-axis
With MN having an infinite slope, it runs parallel to the Y-axis and perpendicular to the X-axis.
Therefore, lines PQ and MN are indeed perpendicular.
Answer:
Step-by-step explanation:
Notation
is the sample mean
indicates the population mean (the variable of interest)
s signifies the sample standard deviation
n denotes the sample size
Solution to the problem
The mean's confidence interval is derived from the following formula:
(1)
In this instance, the 9% confidence interval corresponds to:
We can determine the mean using the following:
Additionally, the margin of error can be calculated as:
The margin of error for this situation is expressed as:
Next, we find the standard error:
The critical value for a 95% confidence interval using a normal standard distribution is roughly 1.96, and substituting gives us:
For the 98% confidence interval, the significance corresponds to and
with a critical value of 2.326, yielding a confidence interval of: