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MAT/STA 325 Exam 2 5 Novemb er, 1997 Prof. Thistleton
(1) The following questions are based up on an exp eriment in which you roll a fair die and count the numb er of times a 2 o ccurs.
- Supp ose that you roll the die 100 times. What is the probability of obtaining a 2 on more than 20% of the rolls?
- Now supp ose that you roll the die 500 times. What is the probability of obtaining a 2 on more than 20% of the rolls?
- Finally, supp ose that you roll the die 1000 times. What is the probability of obtaining a 2 on more than 20% of the rolls?
(2) You are working with 3 colleagues in a lab oratory and are making very sensitive measurements. Supp ose that the p opulation of measurements in your exp eriment is normally distributed. You gather the following data:
Trial 1 2 3 4 Voltage (in volts) 0.38 0.42 0.41 0.
Compute the mean, x, and the standard deviation, s, for this sample data.
Assuming that the p opulation of all such measurements is normally distributed, construct 90% and 99% con dence intervals for the voltage.
(4) You are insp ecting containers of solvent on a pro duction line. In particular, you wish to sample p erio dically from the large numb er of containers for which you are resp onsible in order to ensure that their volumes are very close to their target value. If the p opulation of all such containers has a mean volume of 15.7 gallons and a standard deviation of 0.2 gallons:
What is the probability that an individual chosen at random from this p opulation has a volume b etween 15.6 and 15.8?
What is the probability that a simple random sample of size n = 10 taken from this p opulation has a volume b etween 15.6 and 15.8?
What is the probability that a simple random sample of size n = 50 taken from this p opulation has a volume b etween 15.6 and 15.8?
(5) You obtain the following data from a sample of size n = 31: x = 250 and s = 12.
Construct a 95% con dence interval for , the p opulation standard deviation
Using the ^2 distribution.
Using the normal distribution.
Construct a 95% con dence interval for the p opulation prop ortion, , based up on sample data x = 10 and n = 1000.
