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Maslowich
4 years ago
11

2.

Mathematics
1 answer:
Jet001 [13]4 years ago
3 0

Answer:

119.2

Step-by-step explanation:

Given the following :

Mean (m) = 100 years

Standard deviation (sd) = 15 years

closest to the age of a Galápagos Islands giant tortoise at the 90th percentile of the

distribution?

Obtain the Zscore for 90th percentile (0.90) on the z table = 1.28

Zscore = (X - mean) / standard deviation

1.28 = (X - 100) / 15

1.28 × 15 = X - 100

19.2 = X - 100

19.2 + 100 = X

X = 119.2

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A grading scale is set up for 1000 students' test scores. It assumes the
astra-53 [7]

Answer:

464 students will score between 48 and 75. Using the z-distribution, we measure how many standard deviations each score is from the mean, then find the p-value associated with each score to find the proportion, and from the proportion, we find how many out of 1000.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. 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, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

It assumes the scores are normally distributed with a mean score of 75 and a standard deviation of 15.

This means that \mu = 75, \sigma = 15

How many students will score between 48 and 75?

First we find the proportion, which is the pvalue of Z when X = 75 subtracted by the pvalue of Z when X = 48. So

X = 75

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

Z = \frac{75 - 75}{15}

Z = 0

Z = 0 has a p-value of 0.5

X = 48

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

Z = \frac{48 - 75}{15}

Z = -1.8

Z = -1.8 has a p-value of 0.0359

1 - 0.0359 = 0.4641

Out of 1000:

0.4641*1000 = 464

464 students will score between 48 and 75. Using the z-distribution, we measure how many standard deviations each score is from the mean, then find the p-value associated with each score to find the proportion, and from the proportion, we find how many out of 1000.

7 0
3 years ago
Evaluate for x and y<br> 4x-6y=-26<br> -2x+3y-13
kap26 [50]

Answer:

(x, y) = (- 13/2 + 3/2 * y, y) ,y in mathbb R

Step-by-step explanation:

4x-6y=-26

-2x+3y-13

4x-6y=-26

x=-13/2+3/2y

4(-13/2+3/2y) - 6y=-26

y in mathbb R

x, y) = (- 13/2 + 3/2 * y, y) ,y in mathbb

5 0
1 year ago
What is 5/6 plus 7/8?
irina [24]

Answer:

1  17/24

Step-by-step explanation:

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3 years ago
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