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NemiM [27]
3 years ago
8

Suppose the scores on a test given to all juniors in a school district are normally distributed with a mean of 74 and a standard

deviation of 8. On a separate sheet of paper, draw a Normal Curve and label the mean, standard deviations, and the associated percentages.

Mathematics
1 answer:
ivann1987 [24]3 years ago
7 0

Answer:

\mu -\sigma = 66 , \mu +\sigma = 82

\mu -2\sigma = 58 , \mu +2\sigma = 90

\mu -3\sigma = 50 , \mu +3\sigma = 98

And in the figure attached we see the limits with the percentages associated.

Step-by-step explanation:

For this case we know that the random variable of interest is the scores on a test given to all juniors in a school district follows a normal distribution with the following parameters:

X \sim N(\mu= 74, \sigma =8)

For this case we know from the empirical rule that within one deviation from the mean we have approximately 68.2% of the data, within 2 deviations from the mean we have 95% and within 3 deviation 99.7%

We can find the limits and we got:

\mu -\sigma = 66 , \mu +\sigma = 82

\mu -2\sigma = 58 , \mu +2\sigma = 90

\mu -3\sigma = 50 , \mu +3\sigma = 98

And in the figure attached we see the limits with the percentages associated.

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Is<br>Five times what number plus 10 equals 20<br>​
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Answer:

2

Step-by-step explanation:

5*2=10

10+10=20

or

5*x+10=20

10-10=0

20-10=10

5*x=10

5/5=0

10/5=2

x=2

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3 years ago
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worty [1.4K]
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6 0
3 years ago
Select the values of x that make the inequality x &lt; -2 true.
ANTONII [103]

Answer:

A and B

Step-by-step explanation:

-3 and -2 are the only values less than or = to -2

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8 0
3 years ago
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A researcher surveyed 150 high school students and found that 68% played a musical insturment. What would be a reasonable range
maria [59]

Answer:

The reasonable range for the population mean is (61%, 75%).

Step-by-step explanation:

The interval estimate of a population parameter is an interval of values that consist of the values within which the true value of the parameter lies with a certain probability.

The mean of the sampling distribution of sample proportion is, \hat p.

One of the best interval estimate of population proportion is the 95% confidence interval for proportion,

CI=\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}

Given:

n = 150

\hat p = 0.68

The critical value of <em>z</em> for 95% confidence level is:

z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

Compute the 95% confidence interval for proportion as follows:

CI=\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}

     =0.68\pm1.96\sqrt{\frac{0.68(1-0.68)}{150}}\\\\=0.68\pm 0.0747\\\\=(0.6053, 0.7547)\\\\\approx (0.61, 0.75)

Thus, the reasonable range for the population mean is (61%, 75%).

5 0
3 years ago
What is the simplest form of 4 square root 81x^8y^5?
olasank [31]
Firstly,
thanks for posting this.

81 = 9x9 or 9 squared so at this stage I'm guessing the last two. 
x^ 8 = (x^ 4) x (x^ 2) (its called the multiplication rule of indices). 
Okay I have approx 14 mins to answer.
No panic
√ 81.x^8 x <span>√ y^5
</span>√ (9x^2 x 9x^6) x <span>√ y^5
</span>= 9x x <span>√ 9x^6 x  </span><span>√ y^5
</span>did I just gain time?
√ 9x^6 = <span>√ </span>3x ^3 x <span>√ 3x ^ 3
</span>or 2 . √ 3x^3. <span>√ y^5
</span>more time
okay, so that wasnt successful. 
√ 9x^6 =<span>√ </span> (3x^2) x <span>√ </span>(3x^4)




5 0
3 years ago
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