How can I find the Z score of 0.05?
up vote
0
down vote
favorite
This is the question:
To estimate the average speed of cars on a specific highway, an investigator
collected speed data from a random sample of 75 cars driving on the
highway. The sample mean and sample standard deviation are 58 miles per
hour and 15 miles per hour, respectively.
Construct a 90% confidence interval for the mean speed.
I have the answer for it, and this is the answer:
But, I don't understand why Z0.05 =1.645. On the Standard Normal Distribution Table, P(Z < -1.645) = 0.05. Therefore, Z0.05 should be -1.645 instead of 1.645
probability statistics normal-distribution
asked Apr 21 at 19:27
Rongeegee
102111
add a comment |
up vote
0
down vote
favorite
This is the question:
To estimate the average speed of cars on a specific highway, an investigator
collected speed data from a random sample of 75 cars driving on the
highway. The sample mean and sample standard deviation are 58 miles per
hour and 15 miles per hour, respectively.
Construct a 90% confidence interval for the mean speed.
I have the answer for it, and this is the answer:
But, I don't understand why Z0.05 =1.645. On the Standard Normal Distribution Table, P(Z < -1.645) = 0.05. Therefore, Z0.05 should be -1.645 instead of 1.645
probability statistics normal-distribution
asked Apr 21 at 19:27
Rongeegee
102111
The area under the curve must always be positive. The negative is the $z$ value. What this is saying is that the area under the curve and to the left of the $z$ value is 1.645.
– John Douma
Apr 21 at 19:39
So, Z0.05 means the total area under the curve and to the left of 0.05?
– Rongeegee
Apr 21 at 20:37
Yes, and due to the symmetry of the curve, it is the same as the area to the right of $Z0.95$. You trim 5% of the area from each side to get 90% of the area under the curve.
– John Douma
Apr 21 at 21:13
There is an annoying possibility of confusion in notations such as $Z_{0.05},$ which usually means a z-value that cuts 5% of the probability from the upper tail of the dist'n; that's +1.645. By contrast 'quantile 0.05' cuts 5% prob from the lower tail; that's -1.645. // Software tends to use the 'quantile' notation; printed tables tend to use the 'upper-tail probability' notation.
– BruceET
Apr 21 at 22:31
the standard normal distribution table gives you the area under the curve to the left, why does the table give me 0.5199 when z=0.05.
– Rongeegee
Apr 21 at 22:34
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
This is the question:
To estimate the average speed of cars on a specific highway, an investigator
collected speed data from a random sample of 75 cars driving on the
highway. The sample mean and sample standard deviation are 58 miles per
hour and 15 miles per hour, respectively.
Construct a 90% confidence interval for the mean speed.
I have the answer for it, and this is the answer:
But, I don't understand why Z0.05 =1.645. On the Standard Normal Distribution Table, P(Z < -1.645) = 0.05. Therefore, Z0.05 should be -1.645 instead of 1.645
probability statistics normal-distribution
asked Apr 21 at 19:27
Rongeegee
102111
This is the question:
To estimate the average speed of cars on a specific highway, an investigator
collected speed data from a random sample of 75 cars driving on the
highway. The sample mean and sample standard deviation are 58 miles per
hour and 15 miles per hour, respectively.
Construct a 90% confidence interval for the mean speed.
I have the answer for it, and this is the answer:
But, I don't understand why Z0.05 =1.645. On the Standard Normal Distribution Table, P(Z < -1.645) = 0.05. Therefore, Z0.05 should be -1.645 instead of 1.645
probability statistics normal-distribution
probability statistics normal-distribution
asked Apr 21 at 19:27
Rongeegee
102111
asked Apr 21 at 19:27
Rongeegee
102111
asked Apr 21 at 19:27
Rongeegee
102111
asked Apr 21 at 19:27
Rongeegee
102111
asked Apr 21 at 19:27
Rongeegee
102111
102111
The area under the curve must always be positive. The negative is the $z$ value. What this is saying is that the area under the curve and to the left of the $z$ value is 1.645.
– John Douma
Apr 21 at 19:39
So, Z0.05 means the total area under the curve and to the left of 0.05?
– Rongeegee
Apr 21 at 20:37
Yes, and due to the symmetry of the curve, it is the same as the area to the right of $Z0.95$. You trim 5% of the area from each side to get 90% of the area under the curve.
– John Douma
Apr 21 at 21:13
There is an annoying possibility of confusion in notations such as $Z_{0.05},$ which usually means a z-value that cuts 5% of the probability from the upper tail of the dist'n; that's +1.645. By contrast 'quantile 0.05' cuts 5% prob from the lower tail; that's -1.645. // Software tends to use the 'quantile' notation; printed tables tend to use the 'upper-tail probability' notation.
– BruceET
Apr 21 at 22:31
the standard normal distribution table gives you the area under the curve to the left, why does the table give me 0.5199 when z=0.05.
– Rongeegee
Apr 21 at 22:34
add a comment |
The area under the curve must always be positive. The negative is the $z$ value. What this is saying is that the area under the curve and to the left of the $z$ value is 1.645.
– John Douma
Apr 21 at 19:39
So, Z0.05 means the total area under the curve and to the left of 0.05?
– Rongeegee
Apr 21 at 20:37
Yes, and due to the symmetry of the curve, it is the same as the area to the right of $Z0.95$. You trim 5% of the area from each side to get 90% of the area under the curve.
– John Douma
Apr 21 at 21:13
There is an annoying possibility of confusion in notations such as $Z_{0.05},$ which usually means a z-value that cuts 5% of the probability from the upper tail of the dist'n; that's +1.645. By contrast 'quantile 0.05' cuts 5% prob from the lower tail; that's -1.645. // Software tends to use the 'quantile' notation; printed tables tend to use the 'upper-tail probability' notation.
– BruceET
Apr 21 at 22:31
the standard normal distribution table gives you the area under the curve to the left, why does the table give me 0.5199 when z=0.05.
– Rongeegee
Apr 21 at 22:34
The area under the curve must always be positive. The negative is the $z$ value. What this is saying is that the area under the curve and to the left of the $z$ value is 1.645.
– John Douma
Apr 21 at 19:39
The area under the curve must always be positive. The negative is the $z$ value. What this is saying is that the area under the curve and to the left of the $z$ value is 1.645.
– John Douma
Apr 21 at 19:39
So, Z0.05 means the total area under the curve and to the left of 0.05?
– Rongeegee
Apr 21 at 20:37
So, Z0.05 means the total area under the curve and to the left of 0.05?
– Rongeegee
Apr 21 at 20:37
Yes, and due to the symmetry of the curve, it is the same as the area to the right of $Z0.95$. You trim 5% of the area from each side to get 90% of the area under the curve.
– John Douma
Apr 21 at 21:13
Yes, and due to the symmetry of the curve, it is the same as the area to the right of $Z0.95$. You trim 5% of the area from each side to get 90% of the area under the curve.
– John Douma
Apr 21 at 21:13
There is an annoying possibility of confusion in notations such as $Z_{0.05},$ which usually means a z-value that cuts 5% of the probability from the upper tail of the dist'n; that's +1.645. By contrast 'quantile 0.05' cuts 5% prob from the lower tail; that's -1.645. // Software tends to use the 'quantile' notation; printed tables tend to use the 'upper-tail probability' notation.
– BruceET
Apr 21 at 22:31
There is an annoying possibility of confusion in notations such as $Z_{0.05},$ which usually means a z-value that cuts 5% of the probability from the upper tail of the dist'n; that's +1.645. By contrast 'quantile 0.05' cuts 5% prob from the lower tail; that's -1.645. // Software tends to use the 'quantile' notation; printed tables tend to use the 'upper-tail probability' notation.
– BruceET
Apr 21 at 22:31
the standard normal distribution table gives you the area under the curve to the left, why does the table give me 0.5199 when z=0.05.
– Rongeegee
Apr 21 at 22:34
the standard normal distribution table gives you the area under the curve to the left, why does the table give me 0.5199 when z=0.05.
– Rongeegee
Apr 21 at 22:34
add a comment |
1 Answer
1
active
oldest
votes
up vote
0
down vote
Since the normal distribution is symmetric, the sign of $Z_{alpha /2}$ is not as important as the fact that 5% of the area under the curve is in each tail of the bell curve. Since your confidence interval is constructed by using $$bar{x} pm Z_{alpha /2} frac{s}{sqrt{n}}$$ you will be using both the positive a negative of this Z value.
answered Apr 21 at 19:41
KBerdeguez
1
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Since the normal distribution is symmetric, the sign of $Z_{alpha /2}$ is not as important as the fact that 5% of the area under the curve is in each tail of the bell curve. Since your confidence interval is constructed by using $$bar{x} pm Z_{alpha /2} frac{s}{sqrt{n}}$$ you will be using both the positive a negative of this Z value.
answered Apr 21 at 19:41
KBerdeguez
1
add a comment |
up vote
0
down vote
Since the normal distribution is symmetric, the sign of $Z_{alpha /2}$ is not as important as the fact that 5% of the area under the curve is in each tail of the bell curve. Since your confidence interval is constructed by using $$bar{x} pm Z_{alpha /2} frac{s}{sqrt{n}}$$ you will be using both the positive a negative of this Z value.
answered Apr 21 at 19:41
KBerdeguez
1
add a comment |
up vote
0
down vote
up vote
0
down vote
Since the normal distribution is symmetric, the sign of $Z_{alpha /2}$ is not as important as the fact that 5% of the area under the curve is in each tail of the bell curve. Since your confidence interval is constructed by using $$bar{x} pm Z_{alpha /2} frac{s}{sqrt{n}}$$ you will be using both the positive a negative of this Z value.
answered Apr 21 at 19:41
KBerdeguez
1
Since the normal distribution is symmetric, the sign of $Z_{alpha /2}$ is not as important as the fact that 5% of the area under the curve is in each tail of the bell curve. Since your confidence interval is constructed by using $$bar{x} pm Z_{alpha /2} frac{s}{sqrt{n}}$$ you will be using both the positive a negative of this Z value.
answered Apr 21 at 19:41
KBerdeguez
1
answered Apr 21 at 19:41
KBerdeguez
1
answered Apr 21 at 19:41
KBerdeguez
1
answered Apr 21 at 19:41
KBerdeguez
1
1
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2747779%2fhow-can-i-find-the-z-score-of-0-05%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
The area under the curve must always be positive. The negative is the $z$ value. What this is saying is that the area under the curve and to the left of the $z$ value is 1.645.
– John Douma
Apr 21 at 19:39
So, Z0.05 means the total area under the curve and to the left of 0.05?
– Rongeegee
Apr 21 at 20:37
Yes, and due to the symmetry of the curve, it is the same as the area to the right of $Z0.95$. You trim 5% of the area from each side to get 90% of the area under the curve.
– John Douma
Apr 21 at 21:13
There is an annoying possibility of confusion in notations such as $Z_{0.05},$ which usually means a z-value that cuts 5% of the probability from the upper tail of the dist'n; that's +1.645. By contrast 'quantile 0.05' cuts 5% prob from the lower tail; that's -1.645. // Software tends to use the 'quantile' notation; printed tables tend to use the 'upper-tail probability' notation.
– BruceET
Apr 21 at 22:31
the standard normal distribution table gives you the area under the curve to the left, why does the table give me 0.5199 when z=0.05.
– Rongeegee
Apr 21 at 22:34