Question

Use the following unit normal tables and accompanying figures to determine the probability that a z-score value would fall within each of the specified ranges. To use the tables, click on the Unit Normal Tables tab beneath the figures, and use the dropdown box to select the desired range of z-score values. A table of the proportions of the normal distribution corresponding to that range of z-scores will appear. If you need a different range of z-scores, simply click on the box again and select a new range. Suggestion: For each of the following five questions, make a sketch of the area under the normal distribution you are seeking. This sketch will help you determine which column(s) of the unit normal tables to use in determining the appropriate probability. 1. p(z > 1.2) 2. p(z > -3.4) 3. p(z < 3.8) 4. p(0.9 < z < 1.9) 5. p(-3.2 < z < 1.2)

          Use the following unit normal tables and accompanying figures to determine the probability that a z-score value
would fall within each of the specified ranges. To use the tables, click on the Unit Normal Tables tab beneath the
figures, and use the dropdown box to select the desired range of z-score values. A table of the proportions of the
normal distribution corresponding to that range of z-scores will appear. If you need a different range of z-scores,
simply click on the box again and select a new range.
Suggestion: For each of the following five questions, make a sketch of the area under the normal distribution you are
seeking. This sketch will help you determine which column(s) of the unit normal tables to use in determining the
appropriate probability.
1. p(z > 1.2)
2. p(z > -3.4)
3. p(z < 3.8)
4. p(0.9 < z < 1.9)
5. p(-3.2 < z < 1.2)

Show more…

Use the following unit normal tables and accompanying figures to determine the probability that a z-score value
would fall within each of the specified ranges. To use the tables, click on the Unit Normal Tables tab beneath the
figures, and use the dropdown box to select the desired range of z-score values. A table of the proportions of the
normal distribution corresponding to that range of z-scores will appear. If you need a different range of z-scores,
simply click on the box again and select a new range.
Suggestion: For each of the following five questions, make a sketch of the area under the normal distribution you are
seeking. This sketch will help you determine which column(s) of the unit normal tables to use in determining the
appropriate probability.
1. p(z > 1.2)
2. p(z > -3.4)
3. p(z < 3.8)
4. p(0.9 < z < 1.9)
5. p(-3.2 < z < 1.2)

Added by Philip W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Kari Hasz

09/20/2023

Step 1

P(z > 1.2): This is the probability that z is greater than 1.2. To find this, we look up 1.2 in the z-table, which gives us 0.8849. This is the probability that z is less than 1.2. Since we want the probability that z is greater than 1.2, we subtract this from 1. Show more…

Show all steps

lock

Thanks for your feedback!

Use the following unit normal tables and accompanying figures to determine the probability that a z-score value would fall within each of the specified ranges. To use the tables, click on the Unit Normal Tables tab beneath the figures, and use the dropdown box to select the desired range of z-score values. A table of the proportions of the normal distribution corresponding to that range of z-scores will appear. If you need a different range of z-scores, simply click on the box again and select a new range. Suggestion: For each of the following five questions, make a sketch of the area under the normal distribution you are seeking. This sketch will help you determine which column(s) of the unit normal tables to use in determining the appropriate probability. 1. p(z > 1.2) 2. p(z > -3.4) 3. p(z < 3.8) 4. p(0.9 < z < 1.9) 5. p(-3.2 < z < 1.2)

Play audio

Feedback

Powered by NumerAI

Kari Hasz and 70 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

00:02 For each of the following five questions, make a sketch of the area under the normal distribution you are seeking and then find the appropriate probability.

00:13 So the probability that z is greater than 1 .5, probability that z is greater than negative 3 .4, probability that z is less than 3 .8, probability that z is between 0 .9 and 1 .9, and the probability that z is between negative 3 .2 and positive 1 .2.

00:55 So if this is 1 .5 standard deviations above our mean, the probability that z is greater than means that we're trying to find this area here.

01:12 Now most standard normal distribution tables are going to give you the probability to the left, not to the right.

01:23 So when you look up 1 .5 in your table, you're going to want to subtract that probability or that proportion from 1.

01:32 So we're going to want to take 1 minus 0 .9332 to get our probability, which is 0 .0668.

01:45 So for the probability that z is less than negative 3 .4, so if negative 3 .4, that's 3 .4 standard deviations below the mean, and then we want the probability that z is greater than that.

02:05 Again, when we look up negative 3 .4 in our table, our table is going to give us the probability to the left.

02:13 So we are going to want to take 1 minus 0 .0003 to get our probability, which is 0 .9997.

02:26 Now for the probability that x is less than 3 .8, that's 3 .8 standard deviations above the mean, then this is when we can just look up in the table.

02:41 So when we look up 3 .8 in our standard normal table, the proportion that is there doesn't require any additional calculation...

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