find z such that 6.6% of the standard normal curve lies to the right of z. (Round your answer to two decimal places.)
To find the value of z such that 6.6% of the standard normal curve lies to the right of z, we can use a standard normal distribution table.
Step 1: Subtract 6.6% from 100% to find the area to the left of z.
100% - 6.6% = 93.4%
Step 2: Look up the area of 93.4% in the standard normal distribution table.
From the table, we find that the closest area to 93.4% is 0.934.
Step 3: Find the corresponding z-value for the area of 0.934 in the table.
The closest z-value is approximately 1.50.
Therefore, z ≈ 1.50.
To find the value of z such that 6.6% of the standard normal curve lies to the right of z, we can use a standard normal distribution table or a calculator with a standard normal cumulative distribution function (CDF).
Using a standard normal distribution table:
1. Look for the given percentage in the table. In this case, we are looking for 6.6%, so find the closest value to 6.6% in the table.
2. Locate the corresponding z-value in the same row as the percentage found in step 1. This z-value represents the value for which the probability to the right of z is 6.6%.
Using a calculator with a standard normal cumulative distribution function (CDF):
1. Use the cumulative distribution function (CDF) with the given probability (6.6%) as the argument to find the z-value.
For example, in Python, you can use the "scipy" library:
```
from scipy.stats import norm
z = norm.ppf(1 - 0.066)
```
The `norm.ppf` function calculates the inverse cumulative distribution function (CDF). By subtracting the probability from 1 (`1 - 0.066` in this case), we calculate the probability to the left of z, which is what we need to find for this question.
Regardless of the method used, the resulting z-value represents the value such that 6.6% of the standard normal curve lies to the right of z.
Make sure to round your answer to two decimal places as specified in the question.
The standard normal curve is N(0, 1). That 6.6& of the curve lies right to the desired z means that .944 of it lies to the left.
Use the inverse norm function with the above data in a calculator or look it up in a table. z = +1.589.