Answered

Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

The scores on a standardized exam are normally distributed with a mean of 400 and a standard deviation of 50.

Approximately 40% of the scores are greater than which score?

370

387

413

430

Sagot :

Using the normal distribution, it is found that approximately 40% of the scores are greater than 413.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

In this problem, we have that the mean and the standard deviation of the scores are given by:

[tex]\mu = 400, \sigma = 50[/tex]

Approximately 40% of the scores are greater than the 60th percentile, which is X when Z = 0.253.

Then:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.253 = \frac{X - 400}{50}[/tex]

X - 400 = 50(0.253)

X = 412.65.

Rounding up, approximately 40% of the scores are greater than 413.

More can be learned about the normal distribution at https://brainly.com/question/24663213

#SPJ1

Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.