Answer:
The probability that a randomly selected student’s math score is between 300 and 700 is 0.9544.
Step-by-step explanation:
We have given that, The SAT mathematics scores in the state of Florida are approximately normally distributed with a mean of 500 and a standard deviation of 100.
To find : What is the probability that a randomly selected student’s math score is between 300 and 700?
Solution :
The mean is ![\mu=500](https://tex.z-dn.net/?f=%5Cmu%3D500)
The standard deviation is ![\sigma=1000](https://tex.z-dn.net/?f=%5Csigma%3D1000)
Formula to find z-score is
![z=\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
Now, we have to find the probability score is between 300 and 700
For x = 300 substitute in the formula,
![z = \frac{300-500}{100}\\\\z =-2](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B300-500%7D%7B100%7D%5C%5C%5C%5Cz%20%3D-2)
For x = 700 substitute in the formula,
![z = \frac{700-500}{100}\\\\z =2](https://tex.z-dn.net/?f=z%20%3D%20%5Cfrac%7B700-500%7D%7B100%7D%5C%5C%5C%5Cz%20%3D2)
Now, The probability between P(-2<z<2) is written as
![P(-2](https://tex.z-dn.net/?f=P%28-2%3Cz%3C2%29%3DP%28z%3C2%29-P%28z%3C-2%29)
Using the z table substitute the values of z
At z<-2 is 0.228 and at z<2 is 0.9772.
![P(-2](https://tex.z-dn.net/?f=P%28-2%3Cz%3C2%29%3D0.9772-0.0228)
![P(-2](https://tex.z-dn.net/?f=P%28-2%3Cz%3C2%29%3D0.9544)
Therefore, The probability that a randomly selected student’s math score is between 300 and 700 is 0.9544.