Given a standard normal variable. What is the probability that z lies between 1.48 and 2.13

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability between the Z scores.

To find the probability that a standard normal variable (z) lies between two specific values, we can use the standard normal distribution table or a statistical software.

Here's how you can find the probability manually using a standard normal distribution table:

1. Start by locating the first value, 1.48, in the table. Look for the column headers that represent the whole numbers and find the row that corresponds to the tenths place. In this case, the value of 1.48 falls between the row with 1.4 and 1.5.

2. Next, locate the second value, 2.13, in the table. Again, find the whole number column and the tenths place row. In this case, the value of 2.13 falls between the rows with 2.1 and 2.2.

3. Now, find the probability associated with the first value (1.48) from the table. The intersection point of the row (1.4) and the column (0.08) will give you the probability value. Let's say it is 0.9292.

4. Similarly, find the probability associated with the second value (2.13) from the table. The intersection point of the row (2.1) and the column (0.03) will give you the probability value. Let's say it is 0.9832.

Note: The table gives the probabilities for the left tail of the standard normal distribution. To find the probability between two values, you need to subtract the probability associated with the first value from the probability associated with the second value.

5. Subtract the probability of the first value (0.9292) from the probability of the second value (0.9832):
P(1.48 < z < 2.13) = P(z < 2.13) - P(z < 1.48) = 0.9832 - 0.9292 = 0.054

Therefore, the probability that the standard normal variable z lies between 1.48 and 2.13 is approximately 0.054.

Alternatively, you can also use statistical software or calculators that directly provide probabilities for specific ranges of a standard normal distribution.