Answer:
1/6
Step-by-step explanation:
Answer:
120 deg
Step-by-step explanation:
Answer:
A task time of 177.125s qualify individuals for such training.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
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. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.
In this problem, we have that:
A distribution that can be approximated by a normal distribution with a mean value of 145 sec and a standard deviation of 25 sec, so
.
The fastest 10% are to be given advanced training. What task times qualify individuals for such training?
This is the value of X when Z has a pvalue of 0.90.
Z has a pvalue of 0.90 when it is between 1.28 and 1.29. So we want to find X when
.
So
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![1.285 = \frac{X - 145}{25}](https://tex.z-dn.net/?f=1.285%20%3D%20%5Cfrac%7BX%20-%20145%7D%7B25%7D)
![X - 145 = 32.125](https://tex.z-dn.net/?f=X%20-%20145%20%3D%2032.125)
![X = 177.125](https://tex.z-dn.net/?f=X%20%3D%20177.125)
A task time of 177.125s qualify individuals for such training.
Answer:
I think the answer for the first one is 3 I am not sure about the second one
Answer:
![P(disease/positivetest) = 0.36116](https://tex.z-dn.net/?f=P%28disease%2Fpositivetest%29%20%3D%200.36116)
Step-by-step explanation:
This is a conditional probability exercise.
Let's name the events :
I : ''A person is infected''
NI : ''A person is not infected''
PT : ''The test is positive''
NT : ''The test is negative''
The conditional probability equation is :
Given two events A and B :
P(A/B) = P(A ∩ B) / P(B)
![P(B) >0](https://tex.z-dn.net/?f=P%28B%29%20%3E0)
P(A/B) is the probability of the event A given that the event B happened
P(A ∩ B) is the probability of the event (A ∩ B)
(A ∩ B) is the event where A and B happened at the same time
In the exercise :
![P(I)=0.025](https://tex.z-dn.net/?f=P%28I%29%3D0.025)
![P(NI)= 1-P(I)=1-0.025=0.975\\P(NI)=0.975](https://tex.z-dn.net/?f=P%28NI%29%3D%201-P%28I%29%3D1-0.025%3D0.975%5C%5CP%28NI%29%3D0.975)
![P(PT/I)=0.904\\P(PT/NI)=0.041](https://tex.z-dn.net/?f=P%28PT%2FI%29%3D0.904%5C%5CP%28PT%2FNI%29%3D0.041)
We are looking for P(I/PT) :
P(I/PT)=P(I∩ PT)/ P(PT)
![P(PT/I)=0.904](https://tex.z-dn.net/?f=P%28PT%2FI%29%3D0.904)
P(PT/I)=P(PT∩ I)/P(I)
0.904=P(PT∩ I)/0.025
P(PT∩ I)=0.904 x 0.025
P(PT∩ I) = 0.0226
P(PT/NI)=0.041
P(PT/NI)=P(PT∩ NI)/P(NI)
0.041=P(PT∩ NI)/0.975
P(PT∩ NI) = 0.041 x 0.975
P(PT∩ NI) = 0.039975
P(PT) = P(PT∩ I)+P(PT∩ NI)
P(PT)= 0.0226 + 0.039975
P(PT) = 0.062575
P(I/PT) = P(PT∩I)/P(PT)
![P(I/PT)=\frac{0.0226}{0.062575} \\P(I/PT)=0.36116](https://tex.z-dn.net/?f=P%28I%2FPT%29%3D%5Cfrac%7B0.0226%7D%7B0.062575%7D%20%5C%5CP%28I%2FPT%29%3D0.36116)