Answered

Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Discover in-depth solutions to your questions from a wide range of experts on our user-friendly Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

The summer income of the 3,408 students at Centennial High School last year was
normally distributed with mean $1,751 and standard deviation $421.
Approximately what percent of the students had incomes between $1,000 and $3,000?
Round to the nearest percent? See lesson 1-4 Example 4 if necessary.
O 1.19%
99.85%
O 2.97%
0 27.61%
096.1%

Sagot :

LammettHash

You want to find

P(1000 < X < 3000)

where X is normally distributed with mean 1751 and standard deviation 421. Transform X to Z, so that it follows the standard normal distribution with mean 0 and standard deviation 1 using the relation

X = 1751 + 421Z   ==>   Z = (X - 1751)/421

Then

P(1000 < X < 3000) = P((1000 - 1751)/421 < (X - 1751)/421 < (3000 - 1751)/421)

… ≈ P(-1.783 < Z < 2.967)

… ≈ P(Z < 2.967) - P(Z < -1.783)

… ≈ 0.9985 - 0.0373

… ≈ 0.9612

so that approximately 96.1% of the students fall in this income range.

Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.