High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Assume that adults have scores that are normally distributed with a mean of 97.9 and a standard deviation of 18.6.

Find the first quartile, [tex]Q_1[/tex], which is the IQ score separating the bottom 25% from the top 75%.

(Hint: Draw a graph.)

The first quartile is ______. (Type an integer or decimal rounded to one decimal place as needed.)

Answer :

The first quartile when [tex]\mu = 97.4[/tex] and [tex]\sigma = 17.6[/tex] is [tex]Q_1 = 85.54[/tex] .

In statistics, a quartile is a type of quantile that divides the number of data points into four corridors, or diggings, of more-or-less equal size. The data must be ordered from lowest to largest to cipher quartiles; as similar, quartiles are a form of order statistic.

Let us assume that X is the adult IQ score.

[tex]\mu = 97.4[/tex]

[tex]\sigma = 17.6[/tex]

Let [tex]z_0[/tex] be the z-score for the first quartile.

[tex]P(z\geq z_0 ) = 0.75[/tex]

Now, use the area under the normal curve to find the value of [tex]z_0[/tex] .

[tex]z_0 = -0.674[/tex]

[tex]\frac{X-\mu}{\sigma} = -0.674[/tex]

[tex]\frac{X-97.4}{18.6} = -0.674[/tex]

[tex]X = -0.674\times 18.6 + 97.4[/tex]

[tex]= 85.54[/tex]

Hence, the first quartile is [tex]Q_1 = 85.54[/tex] .

Learn more about quartile here:

https://brainly.com/question/29809572

#SPJ4