Given the points A(-3, -2) and B(12, 3), determine the coordinates of point P on directed line segment stack A B with bar on top
that partitions stack A B with bar on top in a ratio of 3/2.
1 answer:
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Answer:
The time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.
Step-by-step explanation:
We are given that the time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds.
The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition.
<u><em>Let X = time for this event for boys in secondary school</em></u>
SO, X ~ Normal()
The z-score probability distribution for normal distribution is given by;
Z = ~ N(0,1)
where, = mean time = 460 seconds
= standard deviation = 40 seconds
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.
<u>Now, it is given that the fitness association wants to recognize the fastest 10% of the boys with certificates of recognition, which means;</u>
P(X > x) = 0.10 {where x is the required time which boy need to beat}
P( >
) = 0.10
P(Z > ) = 0.10
<em>So, the critical value of x in the z table which represents the top 10% of the area is given as 1.2816, that is;</em>
<em> </em>
<em> </em> = 460 + 51.264 = <u>511.264 seconds</u>
Hence, the time that the boys need to beat in order to earn a certificate of recognition from the fitness association is 511.264 seconds.
Answer:
0.2177 = 21.77% conditional probability that she does, in fact, have the disease
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Test positive
Event B: Has the disease
Probability of a positive test:
90% of 3%(has the disease).
1 - 0.9 = 0.1 = 10% of 97%(does not have the disease). So
Intersection of A and B:
Positive test and has the disease, so 90% of 3%
What is the conditional probability that she does, in fact, have the disease
0.2177 = 21.77% conditional probability that she does, in fact, have the disease