A bank wishes to estimate the mean credit card balance owed by its customers. The population standard deviation is estimated to be $300. If a 98 percent confidence interval is used and an interval of $78 is desired, how many customers should be sampled?A. 725B. 80C. 57D. 320

Answer: B. 80Step-by-step explanation:We know that the formula to find the sample size is given by :-[tex]n=(\dfrac{z^*\cdot\sigma}{E})^2[/tex], where [tex]\sigma[/tex] = population standard deviation.E= margin of error z*= Two -tailed critical z-value Given : Confidence level = 98% =0.98[tex]\alpha=1-0.98=0.02[/tex]Population standard deviation : [tex]\sigma=300[/tex]Also, from z-table for [tex]\alpha/2=0.01[/tex] (two tailed ), the critical will be = [tex]z^*=2.326[/tex]Then, the required sample size must be :[tex]n=(\dfrac{2.326\cdot300}{78})^2\\\\ n=(8.94615)^2\\\\ n=80.0336686391\approx80[/tex]  [To the nearest option]Hence, the required sample size = 80Hence, the correct option is option B. 80