Find z so that 5% of the area under the standard normal curve lies to the right of z.
the answer according to the book is 1.645, anyone got any ideas on how to get this?
I assume you have either a chart for the normal distribution values, some kind of software, or you can use the internet.
Since you want 5% to lie to the right of the z score, then 95% would lie to the left of the z score.
Find .95 in the body of the table and it should be in around 1.645
My favourite is the following webpage, it replaces your old tables from your old textbooks
http://davidmlane.com/normal.html
choose button : Value from an area
In Area: enter .95
click on "below" and "recalculate"
you should see 1.645
btw, enter .05 in area, then click on "above", then "recalculate"
how about that?
ok that makes sense, thanks.
Well, to find the value of z that corresponds to 5% of the area under the standard normal curve lying to the right, you can use a z-table or a calculator.
In this case, since we are looking for the area to the right of z, we need to find the z-value that leaves a total area of 1 - 0.05 = 0.95 to the left of it.
Using a z-table, you can find that the z-value corresponding to an area of 0.95 to the left is approximately 1.645. So, 5% of the area under the standard normal curve lies to the right of z = 1.645.
Now, let me throw in a joke to lighten things up: Why don't scientists trust atoms?
Because they make up everything!
To find the value of z such that 5% of the area under the standard normal curve lies to the right of z, we can use the standard normal distribution table (also known as the Z-table).
1. Look up the value closest to 0.05 in the body of the Z-table. This will give you the area to the left of z.
2. Locate the corresponding z-score (z-value) in the leftmost column of the table.
3. Note that the area to the right of z is equal to 1 minus the area to the left of z.
So, subtract the value found in step 1 from 1 to get the area to the right of z.
Using this method, we find that the closest value to 0.05 in the Z-table is 0.0495.
Subtracting 0.0495 from 1 gives us 0.9505.
Now, find the closest z-score (z-value) in the leftmost column of the table corresponding to the area of 0.9505.
The closest value in the table is 1.64, and the next value is 1.65.
Therefore, the value of z that satisfies the condition is approximately 1.645.
To find the value of z such that 5% of the area under the standard normal curve lies to the right of z, you can use a standard normal distribution table or a statistical calculator.
Here's a step-by-step process to find z:
1. Identify the desired area: The question asks for the area to the right of z, which is 5% or 0.05.
2. Locate the area in the standard normal distribution table: Standard normal distribution tables provide the area to the left of a specific z-value. Since we need the area to the right, subtract the desired area from 1: 1 - 0.05 = 0.95.
3. Locate the closest area in the table: Find the closest value to 0.95 in the body of the table. In this case, 0.9500 falls between z-values 1.64 and 1.65.
4. Determine the value of z: Depending on the level of precision required, you can either round up or down. Rounding up to 1.65 would mean slightly exceeding the 5% requirement, so we round down to 1.645.
Therefore, the value of z such that 5% of the area under the standard normal curve lies to the right of z is approximately 1.645.