how do I find z such it lies 5.3% to the left of the standard normal curve?
Well, finding z with a specific area under the standard normal curve can be a bit like a game of hide-and-seek. You're looking for that elusive z who likes to hang out on the left tip of the curve. To find this z, we need to consult our friend, the standard normal distribution table, or rely on some handy dandy software.
If we trust those tables, we can reverse engineer things. Since you want 5.3% to be to the left, you can say 1 - 0.053 = 0.947. This means that 94.7% is to the left and 5.3% is to the right of the z-score we're seeking.
Now, hunt for the corresponding value of 0.947 in the standard normal distribution table or use software to find the z-score. In this case, it's approximately 1.67 (rounded to two decimal places, my mathematical amigo).
So, z ≈ 1.67. Safe travels, my friend, and keep those numbers on their toes!
To find the z-score such that it lies 5.3% to the left of the standard normal curve, you can use a standard normal distribution table or a calculator with the cumulative distribution function (CDF).
Here are the step-by-step instructions using a standard normal distribution table:
1. Look up the cumulative probability of 5.3% in the body of the table.
2. Find the closest value in the table to 5.3%. If the exact value is not available, use the closest value below 5.3%.
3. Identify the corresponding z-score value in the row and column of the table where the cumulative probability is found.
Alternatively, if you have access to a calculator, you can use the following steps:
1. Use the inverse cumulative distribution function (also called the percent-point function or the quantile function) of the standard normal distribution.
2. Enter the cumulative probability of 5.3% as the argument into the inverse CDF function.
3. The output will be the z-score corresponding to the given cumulative probability.
Either method will provide you with the z-score that lies 5.3% to the left of the standard normal curve.
To find the z-score such that it lies 5.3% to the left of the standard normal curve, you can follow these steps:
1. Look up the cumulative probability in the standard normal distribution table or use a calculator with a built-in normal distribution function. In this case, you would look for the cumulative probability of 0.053 (5.3% expressed as a decimal) to the left of a z-score.
2. If using a standard normal distribution table, locate the row corresponding to the first two digits of the probability (0.05) and the column corresponding to the third digit (0.3). The intersection of these row and column values will give you the z-value.
3. If using a calculator, enter the cumulative probability of 0.053 into the normal distribution function (usually denoted as NORMDIST or NORM.S.DIST) along with a mean of 0 and a standard deviation of 1. The calculator will provide you with the z-score.
By following these steps, you will find the z-score that corresponds to the given cumulative probability and represents the point to the left of it on the standard normal curve.