Mathematics, 01.11.2019 03:31, libby143

The grades on a statistics test are normally distributed with a mean of 62 and q1=52. if the instructor wishes to assign b's or higher to the top 30% of the students in the class, what grade is required to get a b or higher? round your answer to two decimal places.

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answered: Spiderblack212

Probabilities are used to determine the chances of an event.

To get a B or higher, a student needs to score at least 69.76

The given parameters are:

$\mathbf{\mu = 62}$ --- the mean

$\mathbf{x =Q_1 = 52}$ --- the first quartile

From the z-table,

The z score of the first quartile is:

$\mathbf{z = -0.67 }$

The z score formula is:

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

So, we have:

$\mathbf{-0.67 = \frac{52 - 62}{\sigma}}$

$\mathbf{-0.67 = \frac{- 10}{\sigma}}$

Rewrite as:

$\mathbf{\sigma= \frac{- 10}{-0.67 }}$

$\mathbf{\sigma= 14.93}$

To get 30% or above, it means that the p value is:

$\mathbf{p= 1 - 30\%}$

$\mathbf{p= 70\%}$

The z value at $\mathbf{ p= 70\% }$ is

$\mathbf{z = 0.52}\\$

Recall that

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

Substitute $\mathbf{\mu = 62}$ , $\mathbf{z = 0.52}\\$ and $\mathbf{\sigma= 14.93}$

So, we have:

$\mathbf{0.52 = \frac{x - 62}{14.93}}$

Cross multiply

$\mathbf{0.52 \times 14.93= x - 62}$

$\mathbf{7.76 = x - 62}$

Make x the subject

$\mathbf{x = 7.76 + 62}$

$\mathbf{x = 69.76}$

Hence, to get a B or higher, a student needs to score at least 69.76

Read more about probabilities at:

link

answered: nando3024

To get a B or higher, you need to get a grade of at least 69.77.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by

$Z = \frac{X - \mu}{\sigma}$

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.

In this problem, we have that

Mean of 62, so $\mu = 62$

Q1 of 52 means that the z score of X = 52 has a pvalue of 0.25. Z has a pvalue of 0.25 between -0.67 and -0.68, so we use Z = -0.675

$Z = \frac{X - \mu}{\sigma}$

$-0.675 = \frac{52 - 62}{\sigma}$

$-0.675\sigma = -10$

Multiplying the equality by (-1), we have that:

$0.675\sigma = 10$

$\sigma = \frac{10}{0.675}$

$\sigma = 14.8$

If the instructor wishes to assign B's or higher to the top 30% of the students in the class, what grade is required to get a B or higher?

Those are the Z scores that have a pvalue higher than 0.70. So we have to find X when Z has a pvalue of 0.70. This is between 0.52 and 0.53, so we use Z = 0.525

$Z = \frac{X - \mu}{\sigma}$

$0.525 = \frac{X - 62}{14.8}$

X - 62 = 14.8*0.525

X = 69.77

To get a B or higher, you need to get a grade of at least 69.77.

answered: Guest

7. 153.86 ft $^{2}$

8. 12.56 ft $^{2}$

9. 78.5 m $^{2}$

10. 379.94 in $^{2}$

11. 132.665 m $^{2}$

12. 12.56 yd $^{2}$

13. 226.865 ft $^{2}$

14. 113.04 ft $^{2}$

15. 63.585 ft $^{2}$

16. 254.34 m $^{2}$

17. 50.24 cm $^{2}$

step-by-step explanation:

7. $\pi x 7^{2} = \pi * 49 = 153.86 ft^{2}$

8. $\pi * 2^{2} = \pi * 4 = 12.56 ft^{2}$

9. $\pi * 5^{2} = \pi * 25 = 78.5 m^{2}$

10. $\pi * 11^{2} = \pi * 121 = 379.94 in^{2}$

11. $\pi * 6.5^{2} = \pi * 42.25 = 132.665 m^{2}$

12. $\pi * 2^{2} = \pi * 4 = 12.56 yd^{2}$

13. $\pi * 8.5^{2} = \pi * 72.25 = 226.865 ft^{2}$

14. $(\pi /4) * 12^{2} = 0.785 * 144 = 113.04 ft^{2}$

15. $(\pi /4) * 9^{2} = 0.785 * 81 = 63.585 ft^{2}$

16. $(\pi /4) * 18^{2} = 0.785 * 324 = 254.34 m^{2}$

17. $(\pi /4) * 8^{2} = 0.785 * 62 = 50.24 cm^{2}$

Ineed to have answers 6-17 i’m trying to get things done right away so i don’t have to take care of

answered: Guest

3cm and 6 and 9 cm that a possibility of that question
Which are the possible side lengths of a triangle?

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The grades on a statistics test are normally distributed with a mean of 62 and q1=52. if the instruc...