Question

In the example below: i) What is the z-score for a female individual who is 179cm tall? Example 8.1 A Normally Distributed Variable The height (in centimeters) of a large group ($n = 414$) of female general biology students was determined. We will consider this group to be the entire population in which we have an interest. The mean height of this group was 166.8 cm, and the standard deviation was 6.4 cm. Your answer ii) Just by reflecting on the z-score (and its association with standard deviations) without consulting \"Table A.1 Areas of the Normal Distribution\", can you suggest whether this height falls within the 95% range of the population and why?

          In the example below: i) What is the z-score for a female individual who is
179cm tall?
Example 8.1
A Normally Distributed Variable
The height (in centimeters) of a large group ($n = 414$) of
female general biology students was determined. We will
consider this group to be the entire population in which
we have an interest. The mean height of this group was
166.8 cm, and the standard deviation was 6.4 cm.
Your answer
ii) Just by reflecting on the z-score (and its association with standard deviations)
without consulting \"Table A.1 Areas of the Normal Distribution\", can you suggest
whether this height falls within the 95% range of the population and why?

Show more…

In the example below: i) What is the z-score for a female individual who is
179cm tall?
Example 8.1
A Normally Distributed Variable
The height (in centimeters) of a large group (n = 414) of
female general biology students was determined. We will
consider this group to be the entire population in which
we have an interest. The mean height of this group was
166.8 cm, and the standard deviation was 6.4 cm.
Your answer
ii) Just by reflecting on the z-score (and its association with standard deviations)
without consulting T̈able A.1 Areas of the Normal Distribution,̈ can you suggest
whether this height falls within the 95% range of the population and why?

Added by Julio P.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Maxime Rossetti

08/03/2021

Step 1

8 cm) * $\sigma$ is the standard deviation (6.4 cm) Show more…

Show all steps

lock

Thanks for your feedback!

In the example below: i) What is the z-score for a female individual who is 179cm tall? Example 8.1 A Normally Distributed Variable The height (in centimeters) of a large group ($n = 414$) of female general biology students was determined. We will consider this group to be the entire population in which we have an interest. The mean height of this group was 166.8 cm, and the standard deviation was 6.4 cm. Your answer ii) Just by reflecting on the z-score (and its association with standard deviations) without consulting "Table A.1 Areas of the Normal Distribution", can you suggest whether this height falls within the 95% range of the population and why?

Play audio

Feedback

Powered by NumerAI

Maxime Rossetti and 87 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 So we are going to be examining the heights of female students.

00:03 The average is 64 .4 meters, and the standard deviation is 2 .4 meters.

00:10 Just kidding.

00:11 It's inches.

00:13 Now, the z score is looking at x minus me divided by sigma, and that's what we're doing to find the first boundary of x, z is 62.

00:22 So we get approximately negative 1.

00:26 Now for the z score of 63, we're just going to replace the.

00:30 62 to 63.

00:33 But unfortunately i have to write this out again and it's a lot to write out sometimes, but on a test you're going to want to do that.

00:43 And the difference that we find here, or a result, is going to be negative 0 .58.

00:51 So what this tells us is that it is between almost one half and a whole standard deviation below the mean.

01:01 And now to find out what the percentages are, we're just going to look in the back of the book here.

01:08 This one is going to be point...

01:11 Oops.

01:13 Bad trying.

01:14 Bad drawing.

01:16 Okay, there we go.

01:17 Now we're back in order.

01:19 This one is going to be 0 .1587.

01:26 And this other one is going to be a 58 % a much higher 0 .281...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later