Q1

You are a proprieter of NYC boutique. You want to know the average age of your customers. You take a random sampleof 25 customers which yields an average age of 32 yrs with a standard deviationof 8. You have reason to belive the distibution of ages is normally distributed. Determine a 95% confidence interval for the age of your customers.

Q2

The monthly starting salaries of a student that recieved a MBA degree have a standard deviation of $70. What sample size should be selected so that there is 90% confidence of estimating the meanmonthly income within a samplingerror of $15 or less?

Q3

A random variableX has a poissondistribution with prameter u. A sample of 200 observations from this distribution has a mean equal to 3.4. Construct an approximate 90% confidence interval for u.

Q4

A surveyis planned to determine the mean annual family expenses of employees of a large company. The management of the company wishes to be 95% confident that the sample mean is correct within +/- $50 of the true population meanof annual medical expenses. A pilot study indicated the population standard deviation can estiamted to be $400.

a) How large sample size is needed?

b) If management wants to be correct within +/- $25, what sample size is necessary?

Answer:

Q1. Since the distribution of ages is normally distributed, at the 95% level, the critical value is 1.96 by normal distribution table.

So a 95% confidence interval for the age of your customers is [32-1.96*8/sqrt(25), 32+1.96*8/sqrt(25)]=[28.864, 35.136]

Q2. At …

The solution gives detailed steps on solving four questions: finding confidence interval using standard normal distribution.