Mathematics, 08.04.2020 01:57 sportie59

The College Board reported the following mean scores for the three parts of the SAT: Critical reading 502 Mathematics 515 Writing 494 Assume that the population standard deviation on each part of the test is 100. What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test?

Answers: 2

Show answers

Answers

65.78% probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 502, \sigma = 100, n = 90, s = \frac{100}{\sqrt{90}} = 10.54$

What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test?

This is the pvalue of Z when X = 502+10 = 512 subtracted by the pvalue of Z when X = 502-10 = 492.

X = 512

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

By the Central Limit Theorem

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

$Z = \frac{512 - 502}{10.54}$

Z = 0.95

Z = 0.95 has a pvalue of 0.8289

X = 492

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

$Z = \frac{492 - 502}{10.54}$

Z = -0.95

Z = -0.95 has a pvalue of 0.1711

0.8289 - 0.1711 = 0.6578

65.78% probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test.

Answer from: Quest

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

Answer from: Quest

step-by-step explanation:

$\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\\dfrac{m^7n^3}{mn^{-1}}=m^{7-1}n^{)}=m^6n^4$

Another question on Mathematics

Mathematics, 21.06.2019 14:50

What is the square root of 45? (step by step working plz)

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

Cor d? ? me ? max recorded the heights of 500 male humans. he found that the heights were normally distributed around a mean of 177 centimeters. which statements about max’s data must be true? a) the median of max’s data is 250 b) more than half of the data points max recorded were 177 centimeters. c) a data point chosen at random is as likely to be above the mean as it is to be below the mean. d) every height within three standard deviations of the mean is equally likely to be chosen if a data point is selected at random.

Answers: 1

Answer

Mathematics, 22.06.2019 00:00

Cody ran nine miles on his first day of training. the next day he ran 1/8 that distance. how far did he run the second day?

Answers: 2

Answer

Mathematics, 22.06.2019 03:50

Ken leaves work 20 minutes late. he decides to make up time by taking the toll road instead of side streets. he can travel three times faster by taking the toll road. create an equation to represent his total travel time, including wait time, where x is the number of minutes the drive was expected to take

Answers: 2

Answer

You know the right answer?

The College Board reported the following mean scores for the three parts of the SAT: Critical readin...

Questions