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tester [92]
3 years ago
7

The SAT mathematics scores in the state of Florida are approximately normally distributed with a mean of 500 and a standard devi

ation of 100.
Using the empirical rule, what is the probability that a randomly selected student’s math score is between 300 and 700? Express your answer as a decimal.
Mathematics
2 answers:
s2008m [1.1K]3 years ago
6 0
I this the answer you are looking for would probably be 47.7%. hope this helps!!
egoroff_w [7]3 years ago
6 0

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

The standard deviation is  \sigma=1000

Formula to find z-score is

z=\frac{x-\mu}{\sigma}

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

For x = 700 substitute in the formula,

z = \frac{700-500}{100}\\\\z =2

Now, The probability between P(-2<z<2)  is written as

P(-2

Using the z table substitute the values of z

At z<-2 is 0.228 and at z<2 is 0.9772.

P(-2

P(-2

Therefore, The probability that a randomly selected student’s math score is between 300 and 700 is 0.9544.

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