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tester [92]
2 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]2 years ago
6 0
I this the answer you are looking for would probably be 47.7%. hope this helps!!
egoroff_w [7]2 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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Answer:

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Step-by-step explanation:

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⇒ ∠z = 180° - 20°

⇒ ∠z = 160°

The central angle measure equals the corresponding arc measure.

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mote1985 [20]

Step-by-step explanation:

Since X is given to you (in this case, it’s 7), all you have to do is plug it into the equation.

1. -2(7) + 10

When a variable or a number is directly outside a number, it means you should multiply the two numbers, no matter what.

Now that we know this: -2 * 7 = (-14) When a negative is multiplied by a positive, it turns out negative.

2. (-14) + 10: Let’s say (for instance), that I owe 14 dollars to a friend. If I pay 10 of it, how much do I owe my friend? It would be -4 because you’re still in debt, and haven’t payed your friend all of her 14 dollars back.

3. You should come up with an answer of (-4) because of all of the steps given.

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1. (5pt) In a recent New York City marathon, 25,221 men finished and 253 dropped out. Also,
gladu [14]

Answer:

(a) Explained below.

(b) The 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

Step-by-step explanation:

The information provided is:

n (Men who finished the marathon) = 25,221

n (Women who finished the marathon) = 12,883

Compute the proportion of men and women who finished the marathon as follows:

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The combined proportion is:

\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}\\\\=\frac{25221+12883}{38520}\\\\=0.989

(a)

The hypothesis is:

<em>H</em>₀: The rate of those who finish the marathon is the same for men and women, i.e. <em>p</em>₁ - <em>p</em>₂ = 0.

<em>Hₐ</em>: The rate of those who finish the marathon is not same for men and women, i.e. <em>p</em>₁ - <em>p</em>₂ ≠ 0.

Compute the test statistic as follows:

Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)\cdot [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}

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The <em>p</em>-value of the test is more than the significance level. The null hypothesis was failed to be rejected.

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Compute the 99% confidence interval for the difference between proportions as follows:

The critical value of <em>z</em> for 99% confidence level is 2.58.

CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}

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Thu, the 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

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