Answer:
Step-by-step explanation:
By definition if two events are mutually exclusive then they are disjoint events, that is, they can not occur at the same time.
In general terms we say that events are mutually exclusive, then:
In this case we have that
But A and B are mutually exclusive events, then
The value of the P(A∩B) is equal to 0.04.
We have given that,
P(A)= 0.4 and P(B) = 0.85.
We have to determine the P(A and B)
<h3>What is the formula for Independent Events?</h3>For Independent Events,
P(A) × P(B) = P(A∩B)
so we have, P(A∩B) = 0.4×0.1
P(A∩B) = 0.04
P(A') = 1 - 0.4 = 0.6
This information can be represented on a Venn diagram as shown below
P(A'∪B) means the union of everything that is not A with everything that is B
P(A'∪B) = 0.06 + 0.54 + 0.04
P(A'∪B) = 0.64
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Answer: 0.002718
Step-by-step explanation:
Given : The population mean annual salary for environmental compliance specialists is about $62,000.
i.e.
Sample size : n= 32
Let x be the random variable that represents the annual salary for environmental compliance specialists.
Using formula , the z-value corresponds to x= 59000 will be :
Now, by using the standard normal z-table , the probability that the mean salary of the sample is less than $59,000 :-
Hence, the probability that the mean salary of the sample is less than $59,000= 0.002718