Answer :
The correct z-value for a 94.8% confidence interval is not listed, but the closest approximate z-value given the options is 1.64, as it is slightly less than the z-value for a 95% confidence interval, which is 1.96.
The student is seeking the z-value for a 94.8% confidence interval. In statistics, z-values are associated with the standard normal distribution and tell us how many standard deviations away from the mean a particular value lies. They are crucial when constructing confidence intervals.
For a 95% confidence interval, the z-value is known to be approximately 1.96. Since a 94.8% confidence interval is very close to 95%, the z-value should be slightly less than 1.96. Looking at the options given, the closest z-value below 1.96 is 1.645 for a 90% confidence interval. However, for a 94 to 95% confidence interval, typical z-values range from about 1.64 to 1.96.
Consequently, neither 1.63 nor 1.645 is a correct fit for a 94.8% confidence interval, whereas 1.64 is slightly nearer to the correct value but not as accurate as 1.96, which is too high. The correct z-value is not listed in the options provided but it would be slightly less than the z-value for a 95% confidence interval.
Therefore, given the provided options b, 1.64 is likely the closest approximate z-value for a 94.8% confidence interval estimation.
