. An admissions officer has determined that the population of applicants to the MBA program has undergraduate GPA’s that are approximately normally distributed with standard deviation .45. A random sample of 25 applicants for next fall has a sample mean GPA of 3.30. Find the 95% confidence interval for the mean GPA among applicants to this MBA.2. A production process fills containers by weight. Weights of containers are approximately normally distributed. Historically, the standard deviation of weights is 5.5 ounces. (This standard deviation is therefore known.) How large a sample would be required in order for the 99% confidence interval for to have a length of 2 ounces?
Accepted Solution
A:
Answer:Step-by-step explanation:a) Let X be the population of applicants to the MBA program has undergraduate GPAâ€X is N(mu,0.45)Sample size n = 3.3[tex]\bar x =3.3[/tex]Since population std dev is known z value can be usedMargin of error =[tex]1.96*\frac{0.45}{\sqrt{25} }\\ =0.1764[/tex]Confidence interval =[tex](3.3-0.1764,3.3+0.1764)\\=(3.1236,3.1764)[/tex]b) X weight of containers is N(mu,0.5.5)Sample size n = ?Since population std dev is known z value can be usedMargin of error =[tex]2.58*\frac{5.5}{\sqrt{n} }=2\\\\n=50.339[/tex]n=51