Answer: 0.0548
Step-by-step explanation:
Given, A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = 0.05.
Let 
represents the sample mean GPA for each student.
Then, the probability that the random sample of 100 male students has a mean GPA greater than 3.42:
![P(\overline{X}>3.42)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{3.42-3.5}{\dfrac{0.5}{\sqrt{100}}})\\\\=P(Z>\dfrac{-0.08}{\dfrac{0.5}{10}})\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=P(Z>1.6)\\\\=1-P(Z](https://tex.z-dn.net/?f=P%28%5Coverline%7BX%7D%3E3.42%29%3DP%28%5Cdfrac%7B%5Coverline%7BX%7D-%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D%3E%5Cdfrac%7B3.42-3.5%7D%7B%5Cdfrac%7B0.5%7D%7B%5Csqrt%7B100%7D%7D%7D%29%5C%5C%5C%5C%3DP%28Z%3E%5Cdfrac%7B-0.08%7D%7B%5Cdfrac%7B0.5%7D%7B10%7D%7D%29%5C%20%5C%20%5C%20%5BZ%3D%5Cdfrac%7B%5Coverline%7BX%7D-%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D%5D%5C%5C%5C%5C%3DP%28Z%3E1.6%29%5C%5C%5C%5C%3D1-P%28Z%3C1.6%29%5C%5C%5C%5C%3D1-0.9452%3D0.0548)
hence, the required probability is 0.0548.
Answer: G and F are mutually exclusive because they cannot occur together
Step-by-step explanation:
According to the definition of mutually exclusive events,
The events which can not occur together and probability of them occurring together is 0 are known as mutually exclusive events.
The first statement gives an implication that if one happens then other happens meaning they could both still happen so it is not true.
The second statement contradict the question about being mutually exclusive events.
The third statement also is a implication that if one event occurs then other does or does not occur.
The last statement is correct one that conforms with the question and obeys the definition of mutually exclusive events.
Answer:
30 million
Step-by-step explanation:
i just spared my question to get the answer. it is 30 million. have a good day.
<h3>
Answer: Choice H) 2</h3>
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Explanation:
Recall that the pythagorean trig identity is 
If we were to isolate sine, then,
We don't have to worry about the plus minus because sine is positive when 0 < x < pi/2.
Through similar calculations, 
Cosine is also positive in this quadrant.
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So,
Therefore,
is an identity as long as 0 < x < pi/2
Answer:
no
Step-by-step explanation:
To be a function, the x values must correspond to one and only one y value.
In the coordinates given, (0.3, 0.6) and (0.3, 0.7) have the same x- value.
That means that they cannot be a function.
