Mathematics, 22.04.2020 00:28 BluSeaa

Suppose the test scores for a college entrance exam are normally distributed with a mean of 450 and a s. d. of 100. a. What is the probability that a student scores between 350 and 550? b. If the upper 3% scholarship, what score must a student receive to get a scholarship? c. Find the 60th percentile of the test scores. d. Find the middle 30% of the test scores.

Answers: 1

Show answers

Answers

Answer from: linnialmira

a) 68.26% probability that a student scores between 350 and 550

b) A score of 638(or higher).

c) The 60th percentile of test scores is 475.3.

d) The middle 30% of the test scores is between 411.5 and 488.5.

Step-by-step explanation:

Problems of normally distributed samples are 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:

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

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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 450, \sigma = 100$

a. What is the probability that a student scores between 350 and 550?

This is the pvalue of Z when X = 550 subtracted by the pvalue of Z when X = 350. So

X = 550

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

$Z = \frac{550 - 450}{100}$

Z = 1

Z = 1 has a pvalue of 0.8413

X = 350

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

$Z = \frac{350 - 450}{100}$

Z = -1

Z = -1 has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

68.26% probability that a student scores between 350 and 550

b. If the upper 3% scholarship, what score must a student receive to get a scholarship?

100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So it is X when Z = 1.88

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

$1.88 = \frac{X - 450}{100}$

X - 450 = 1.88*100

X = 638

A score of 638(or higher).

c. Find the 60th percentile of the test scores.

X when Z has a pvalue of 0.60. So it is X when Z = 0.253

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

$0.253 = \frac{X - 450}{100}$

X - 450 = 0.253*100

X = 475.3

The 60th percentile of test scores is 475.3.

d. Find the middle 30% of the test scores.

50 - (30/2) = 35th percentile

50 + (30/2) = 65th percentile.

35th percentile:

X when Z has a pvalue of 0.35. So X when Z = -0.385.

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

$-0.385 = \frac{X - 450}{100}$

X - 450 = -0.385*100

X = 411.5

65th percentile:

X when Z has a pvalue of 0.35. So X when Z = 0.385.

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

$0.385 = \frac{X - 450}{100}$

X - 450 = 0.385*100

X = 488.5

The middle 30% of the test scores is between 411.5 and 488.5.

Answer from: Quest

answer:

sometimes

*i think

Answer from: Quest

5050

hope this !

Another question on Mathematics

Mathematics, 21.06.2019 15:40

Yo y do yall have 2 stars that means yall wrong bro

Answers: 1

Answer

Mathematics, 21.06.2019 15:50

If you shift the linear parent function, f(x)=x, up 13 units, what is the equation of the new function?

Answers: 1

Answer

Mathematics, 21.06.2019 16:00

You eat 8 strawberries and your friend eats 12 strawberries from a bowl. there are 20 strawberries left. which equation and solution give the original number of strawberries?

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

In need of in the diagram, ∠abc is a right angle. ∠dbc = 30°27'40". find the measure of ∠abd.

Answers: 1

Answer

You know the right answer?

Suppose the test scores for a college entrance exam are normally distributed with a mean of 450 and...

Questions

Mathematics, 20.01.2021 14:00

Kim is 5 years older than Scott. Kim's mum is 3 times Kim's age. Scott's dad is 3 times Scott's age. How much older is Kim's mum than Scott's dad. Plz...

Mathematics, 20.01.2021 14:00