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STA 100 Quiz 2 13 November, 2003 Prof. Thistleton
I understand that this quiz maybe done with our textbook, mynotes, and a calculator. I received no help from anyindividual, I did not discuss the the exam with anyone, and the work which follows is entirelymyown.
I also understand that the due date for the quiz is November 18th during class and that late papers will not be accepted.
signed date
- What percentage of the area under a normal curve lies between ฮผ โ ฯ and ฮผ + 2ฯ?
- A population of weights is normallydistributed with mean ฮผ = 5 lbs and standard deviation ฯ = 3 lbs. (In our notation from class, the distribution is N (ฮผ = 5, ฯ^2 = 9)). What proportion of weights is between 4 and 7?
- Suppose a population is distributed normallywith mean ฮผ and standard deviation ฯ = 3. If the proportion of data above 10 is 0.2005 (20.05%), what is the mean of the population?
- The number of steaks (a discrete quantity) sold at a certain restaurant on a Friday night is approximatelynormallydistributed with mean ฮผ = 30 and standard deviation ฯ = 10. What is the probabilitythat the restaurant will run out of steaks if it has 50 in its freezer?
- You want to determine whether a coin is fair or not. You have been told that it is, indeed fair.
(a) Calculate the probabilityof obtaining 12 heads on 20 tosses with a fair coin using the formula for a binomial random variable.
(b) Calculate the same probabilityusing the normal approximation to the binomial distri- bution.
(c) Being patient, you tossed the coin 1000 times and obtained 550 heads. What is the probabilityof obtaining 550 or more heads with a fair coin? Are you lead to believe that the coin is fair?
- A population is normallydistributed. If you obtain the data n = 121 and s = 35
(a) Calculate a 95% confidence interval for the population standard deviation using the ฯ^2 distribution
(b) (5 points extra credit) Use the large sample approximation to calculate the same confi- dence interval. (i.e. You will use the Z table).
- A population of test scores is normallydistributed with a mean of 500 and a standard deviation of 100.
(a) Calculate the probabilitythat a randomlyselected individual from this population will have a score greater than 550 points.
(b) Calculate the probabilitythat a simple random sample of size 10 drawn from this pop- ulation will have a mean score greater than 550 points.
(c) Calculate the probabilitythat a simple random sample of size 50 drawn from this pop- ulation will have a mean score greater than 550 points.
