Answer :
To construct a 90% confidence interval, the z* value closest to the cumulative area of 0.9500 in the z-table is 1.645. Thus, the correct answer is 1.64 after rounding. So the correct option (A)
Calculating the z* Value for a 90% Confidence Interval
To construct a 90% confidence interval, you need to find the z* value (also known as the critical value) that corresponds to the middle 90% of the normal distribution. This implies that there is 5% in each tail of the distribution outside of the confidence interval because the normal distribution is symmetrical.
Looking at our z-table, we can find values close to 0.9500 in the body of the table (since we want the middle 90% and 1 - 0.10 = 0.90, we look for 0.9500 to account for one half of the distribution). The z-value closest to this area in the z-table is 1.645, which corresponds to an area of 0.9505. Therefore, the z* value that should be used to construct a 90% confidence interval is 1.645.
So, the correct answer from the provided options would be: 1.64 (since options are rounded to two decimal places).
