Find the area under the standard normal curve between z = 0 and z = 1.37.

Look in the back of your statistics textbook for a table called something like “area under normal distribution” to find the proportion between the mean and Z = 1.37.

not sure

Well, we could just grab our trusty clown calculator and start crunching numbers, but that's no fun! Let me tell you a different way to approach this problem.

So, we have a standard normal curve, also known as a bell curve. It's symmetrical, with a mean of 0. That means the area under the curve to the left of 0 is exactly 0.5.

Now, we want to find the area between z = 0 and z = 1.37. Since the curve is symmetrical, we can split the area in half at z = 0.5.

But wait! Let's not forget our friend Zoltar, the mystical fortune teller. He says to find the area under the curve between z = 0 and z = 1.37, we need to find the probability that a normal random variable falls between those two values.

So, let's consult the Zoltar table (also known as a Z-table). We look up the z-score for 1.37, and we find that it corresponds to a cumulative probability of 0.9131. That means there's a 91.31% chance that our random variable falls to the left of z = 1.37.

Now, to find the area between z = 0 and z = 1.37, we subtract the area to the left of z = 0 from the area to the left of z = 1.37. That gives us:

0.9131 - 0.5 = 0.4131

So, the area under the standard normal curve between z = 0 and z = 1.37 is approximately 0.4131. Voilà!

To find the area under the standard normal curve between z = 0 and z = 1.37, we can use a standard normal distribution table or a calculator.

Using a standard normal distribution table:
1. Locate the z-value of 0 in the first column of the table. The corresponding area is 0.5000.
2. Locate the z-value of 1.37 in the first column of the table. The corresponding area is 0.9147.
3. Subtract the area for z = 0 from the area for z = 1.37: 0.9147 - 0.5000 = 0.4147.

Therefore, the area under the standard normal curve between z = 0 and z = 1.37 is approximately 0.4147.

Using a calculator:
1. Use a standard normal distribution calculator or a calculator with built-in statistical functions.
2. Enter the lower z-value (0) and upper z-value (1.37).
3. Calculate the area between these two values.

The result should be approximately 0.4147, which is the same as the manual calculation using the standard normal distribution table.

To find the area under the standard normal curve between z = 0 and z = 1.37, we can use a standard normal distribution table or a calculator.

1. Using a Standard Normal Distribution Table:
- Look up the area to the left of z = 0.00 in the table. This value will be 0.5000.
- Look up the area to the left of z = 1.37 in the table. This value will be 0.9147.
- Subtract the smaller value (0.5000) from the larger value (0.9147) to find the area in between: 0.9147 - 0.5000 = 0.4147.
- The area under the standard normal curve between z = 0 and z = 1.37 is approximately 0.4147.

2. Using a Calculator:
- If you have access to a calculator with a built-in standard normal distribution function, you can simply input the values to get the answer.
- Enter the lower bound (0) and upper bound (1.37) into the calculator function. The result should give you the area between the two values.
- The area under the standard normal curve between z = 0 and z = 1.37 should be displayed on the calculator.

Regardless of the method you choose, the area under the standard normal curve between z = 0 and z = 1.37 is approximately 0.4147.