Final answer:
The value of d that corresponds to P(z>d)=0.9724 in a standard normal distribution is approximately 1.90. This value is found by looking up the area to the right (1 - 0.9724) in the z-table, which gives the corresponding z-score.
Step-by-step explanation:
Finding the z-score when P(z>d)=0.9724
When given that P(z>d)=0.9724, we are looking for the value of d on the standard normal distribution which leaves an area of 0.9724 to the left of it. Since the z-scores follow a standard normal distribution with a mean of 0 and a standard deviation of 1, we can look up the value in a z-table which provides the area to the left of a z-score.
To find the exact value of d, we look for the area closest to 1 - 0.9724 = 0.0276 in the z-table, which corresponds to the area to the right. The z-score that corresponds to an area to the right of 0.0276 (area to left is 0.9724) is approximately 1.90 according to most z-tables. This z-score is the value of d which we were looking for.
It's important to keep in mind that we are calculating d using the symmetry of the normal distribution, and the fact that the total area under the curve equals 1.