Question

. 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?

Answer 1

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

`\bar x =3.3`

Since population std dev is known z value can be used

Margin of error =
`1.96*(0.45)/(√(25) )\\ =0.1764`

Confidence interval =
`(3.3-0.1764,3.3+0.1764)\\=(3.1236,3.1764)`

b) X weight of containers is N(mu,0.5.5)

Sample size n = ?

Since population std dev is known z value can be used

Margin of error =
`2.58*(5.5)/(√(n) )=2\\\\n=50.339`

n=51