Final answer:
The value of P(1.10 ≤ z ≤ 1.75) in a standard normal distribution is determined by finding the difference between the areas to the left of z = 1.75 and z = 1.10. This can be done using a z-table or a statistical function on a calculator.
Step-by-step explanation:
The value of P(1.10 ≤ z ≤ 1.75) in a standard normal distribution can be found by looking at a z-table or using a calculator with statistical functions. Essentially, you are trying to find the probability that z falls between 1.10 and 1.75. First, you find the area to the left of z = 1.75 and the area to the left of z = 1.10 using the table or calculator. Then, to find P(1.10 ≤ z ≤ 1.75), you subtract the area to the left of z = 1.10 from the area to the left of z = 1.75.
If a z-table or calculator is not available, you can use the fact that the mean and standard deviation of a standard normal distribution are 0 and 1, respectively. For example, if you use a TI-83, 83+, or 84+ calculator, the commands invNorm(0.6554,0,1) and invNorm(0.9591,0,1) would give the z-scores for the left-side areas of 0.6554 and 0.9591, which correspond to z = 1.10 and z = 1.75, respectively. The difference between these areas gives the probability P(1.10 ≤ z ≤ 1.75).