Find confidence interval using standard normal distribution
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Q1
You are a proprieter of NYC boutique. You want to know the average age of your customers. You take a random sample of 25 customers which yields an average age of 32 yrs with a standard deviation of 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 mean monthly income within a sampling error of $15 or less?
Q3
A random variable X has a poisson distribution 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 survey is 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?
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Solution Summary
The solution gives detailed steps on solving four questions: finding confidence interval using standard normal distribution.
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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 ...
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