Question

Scores for a common standardized college aptitude test are normally distributed with a mean of 499 and a standard deviation of 97. Randomly selected men are given a Test Prepartion Course before taking this test. Assume, for sake of argument, that the test has no effect. If 1 of the men is randomly selected, find the probability that his score is at least 563.7. P(X > 563.7) = Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted. If 9 of the men are randomly selected, find the probability that their mean score is at least 563.7. P(M > 563.7) = Enter your answer as a number accurate to 4 decimal places. If the random sample of 9 men does result in a mean score of 563.7, is there strong evidence to support the claim that the course is actually effective? No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 563.7. Yes. The probability indicates that is is (highly ?) unlikely that by chance, a randomly selected group of students would get a mean as high as 563.7.

211

likes

1057 views

Answer to a math question Scores for a common standardized college aptitude test are normally distributed with a mean of 499 and a standard deviation of 97. Randomly selected men are given a Test Prepartion Course before taking this test. Assume, for sake of argument, that the test has no effect. If 1 of the men is randomly selected, find the probability that his score is at least 563.7. P(X > 563.7) = Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted. If 9 of the men are randomly selected, find the probability that their mean score is at least 563.7. P(M > 563.7) = Enter your answer as a number accurate to 4 decimal places. If the random sample of 9 men does result in a mean score of 563.7, is there strong evidence to support the claim that the course is actually effective? No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 563.7. Yes. The probability indicates that is is (highly ?) unlikely that by chance, a randomly selected group of students would get a mean as high as 563.7.

$Expert avatar$

Maude

4.7

107 Answers

Given:

X \sim N(499, 97^2)

We need to find:
1.

P(X > 563.7)

P(M > 563.7)

, where

is the mean of a sample of size

n = 9

Step 1: Calculate the z-score:

z = \frac{563.7 - 499}{97} = \frac{64.7}{97} \approx 0.6680

P(X > 563.7) = P\left(Z > \frac{563.7 - 499}{97}\right) = P(Z > 0.6680) \approx 0.2525

Step 2: For the sample mean with

n = 9

\sigma_M = \frac{97}{\sqrt{9}} = \frac{97}{3}

z_M = \frac{563.7 - 499}{\frac{97}{3}} = \frac{64.7}{\frac{97}{3}} \approx 2

P(M > 563.7) = P\left(Z > \frac{563.7 - 499}{97/3}\right) = P\left(Z > 2\right) \approx 0.0228

Therefore,
1.

P(X > 563.7) \approx \boxed{0.2525}

P(M > 563.7) \approx \boxed{0.0228}

Since the probability of obtaining a sample mean of 563.7 or higher by chance alone is 0.0228, it is unlikely by chance alone, supporting the claim that the course is effective.

Hence, the answer is:
Yes. The probability indicates that it is highly unlikely that by chance, a randomly selected group of students would get a mean as high as 563.7.

Frequently asked questions (FAQs)

Find the limit as x approaches 2 of [(3x+5)/(x+2)] * [(4x-1)/(x-2)].

Math Question: Find the basic shape of the graph of the equation y = x^3 - 2x^2 + x.

In a two-dimensional vector space, if vector A has magnitude 3 and vector B has magnitude 4, what is the magnitude of the vector A multiplied by vector B?

New questions in Mathematics

A particular employee arrives at work sometime between 8:00 a.m. and 8:40 a.m. Based on past experience the company has determined that the employee is equally likely to arrive at any time between 8:00 a.m. and 8:40 a.m. Find the probability that the employee will arrive between 8:05 a.m. and 8:30 a.m. Round your answer to four decimal places, if necessary.

2+2

(3x^(2) 9x 6)/(5x^(2)-20)

We have spent 1/4 of the inheritance on taxes and 3/5 of the rest on buying a house. If the inheritance was a total of €150,000 How much money do we have left?

Find the derivatives for y=X+1/X-1

A warehouse employs 23 workers on first shift, 19 workers on second shift, and 12 workers on third shift. Eight workers are chosen at random to be interviewed about the work environment. Find the probability of choosing exactly five first -shift workers.

Solve the following equation for x in exact form and then find the value to the nearest hundredths (make sure to show your work): 5e3x – 3 = 25

In a company dedicated to packaging beer in 750 mL containers, a normal distribution is handled in its packaging process, which registers an average of 745 mL and a standard deviation of 8 mL. Determine: a) The probability that a randomly selected container exceeds 765 mL of beer b) The probability that the beer content of a randomly selected container is between 735 and 755 mL.

Quadratic equation 2X = 15/X + 7

On+January+10+2023+the+CONSTRUCTORA+DEL+ORIENTE+SAC+company+acquires+land+to+develop+a+real estate+project%2C+which+prev%C3% A9+enable+50+lots+for+commercial+use+valued+in+S%2F+50%2C000.00+each+one%2C+the+company+has+as+a+business+model+generate+ cash+flow+through%C3%A9s+of+the+rental%2C+so+47%2C+of+the+50+enabled+lots+are+planned to lease+47%2C+and+ the+rest+will be%C3%A1n+used+by+the+company+for+management%C3%B3n+and+land+control

cube root of 56