Question

The standard normal table gives areas under the curve to the left of z-scores.

Find the probability in the standard normal table that a value is to the left of 1.9.

Find the probability in the standard normal table that a value is to the left of 0.4.

Subtract the probability of a value being to the left of 0.4 from the probability of a value being to the left of 1.9.

Answer 1

The z-table can be used to find the probability that a value is to the left of a given z-score. The probability that a value is to the left of 1.9 is approximately 0.9713, and the probability that a value is to the left of 0.4 is approximately 0.6554. By subtracting these two probabilities, the probability of a value being between 0.4 and 1.9 is approximately 0.3159.

Step-by-step explanation:

The probability that a value is to the left of a given z-score can be found using the standard normal table, also known as the z-table. The z-table gives the area under the normal curve to the left of a specific z-score.

To find the probability that a value is to the left of 1.9, we need to locate the z-score 1.9 on the z-table and read off the corresponding area.

Using the z-table, we find that the area to the left of 1.9 is approximately 0.9713. Therefore, the probability that a value is to the left of 1.9 is 0.9713.

Similarly, to find the probability that a value is to the left of 0.4, we locate the z-score 0.4 on the z-table and read off the corresponding area.

Using the z-table, we find that the area to the left of 0.4 is approximately 0.6554. Therefore, the probability that a value is to the left of 0.4 is 0.6554.

To subtract the probability of a value being to the left of 0.4 from the probability of a value being to the left of 1.9, we simply subtract the two probabilities. Subtracting 0.6554 from 0.9713, we get 0.3159.

Therefore, the probability of a value being between 0.4 and 1.9 is 0.3159.