Answer:
Step-by-step explanation:
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Let X the random variable that represent the Student scores on exams given by a certain instructor, we know that X have the following distribution:
The sampling distribution for the sample mean is given by:
The deduction is explained below we have this:
Since the variance for each individual observation is 
then:
And then for this special case:
We are interested on this probability:
And we have already found the probability distribution for the sample mean on part a. So on this case we can use the z score formula given by:
Applying this we have the following result:
And using the normal standard distribution, Excel or a calculator we find this:
Answer:
C. 364.4
E. 14
F. 21
G. 96°
Answer:
About 41.5%
Step-by-step explanation:
<em>Given:</em>
<em>A bowl has 8 green grapes and 15 red grapes. Henry randomly chooses a grape, eats it, and then chooses another grape.</em>
<em>To Find:</em>
<em>What is the probability that both grapes are red?</em>
<em>Answer choices:</em>
<em>about 39.7%</em>
<em>about 41.5%</em>
<em>about 42.5%</em>
<em>about 44.5%</em>
<em>Solution:</em>
<em>Since, there are 8 green grapes and 15 red grapes, the total number of grapes is 23 .</em>
<em>As the red grapes are 15..</em>
<em>Thus,</em>
<em>The probability of choosing a red grape the first time is 15/23.</em>
<em>Because out of the total 23 grapes only 15 were red grape.</em>
<em>The probability of choosing the red grape the second time will be 14/22. Because the number of red grapes has already decreased by one and so is the total number of grapes after first choice</em>
<em>Hence, the probability of choosing or eating two red grapes will be :</em>
<em>15/23×14/22</em>
<em>=105/253</em>
<em>=0.415</em>
<em>= 41.5%</em>
<em>Therefore, the probability that both grapes are red is about 41.5%</em>
Answer:
$19.2
Step-by-step explanation:
20% of 8 is 1.6 (let me know if you need me to explain how to find that).
This means that, with a 20% discount, the price of a ticket would be $6.4.
If there are three of you, multiply 6.4 by 3.
That gets you to 19.2
Answer:
(x + 7)^2 = 64
Step-by-step explanation:
x^2 + 23x – 19 = 9x - 4
x^2 + 23x - 9x = -4 + 19
x^2 + 14x = 15 = 0
Completing the square:
(x + 14/2)^2 - (14/2)^2 = 15
(x + 7)^2 - 49 = 15
(x + 7)^2 = 64
