Statistics and Probability Answers

Suppose a regional computer centre A wants to evaluate the performance of its disk memory system. One measure of performance is the average time between failures of its disk drive. To estimate this value, the centre recorded the time between failures for a random sample of 45 disk-drive failures. The following sample statistics were computed: bar x 1768 hours, s = 213 hours
i. Estimate the true mean time between failures with a 90% confidence interval.
ii. If the disk memory system is running properly, the true mean time between failures will exceed 1700 hours. Based on the interval in part (i), what can you infer about the disk memory system?
iii. How large a sample would have been required to achieve 99% confidence interval that the margin of error of estimate would be 20?
iv. Another sample of 50 disk-drive failures has been recorded from another computer centre B. The mean that obtained is 1720 with standard deviation 218. Estimate the difference of the true mean time failures with a 90% confidence inte

The diameter of a brand of ping-pong balls is normally distributed with a mean of 1.3 inches. The population standard deviation is known to be 0.08 inches.
a. Compute the standard error of the mean for sample size of n=25 balls.
b. If the sample size in part a. is decreased what will happen to the size of the standard error of the mean?
c. Suppose a random sample of 25 balls is selected. What id the probability the simple random sample will provide a sample mean within 0.02 of the population mean.
d. If the sample size in part c. is increased what will happen to the probability that the sample mean is within the specified range?

The amount of time that the battery of a certain brand of computer functions is a random
variable with mean 12 hours and standard deviation of 1.5 hours. A random sample of 45
batteries of a certain brand of computer is selected from a normal population. Let X be the
mean time of the battery of a certain brand of computer functions. Find

i. the mean and the standard deviation of X . [3 marks]
ii. the probability that 11.99 < x < 12.02. [3.5 marks]

[Note: Leave all the calculations in 4 decimal places.]

what is the chance of throwing 5 with an ordinary dice ?

An investor wants to make a decision which depends on the state of a country's economy. The probability that the economy will be strong, P(A) is 0.80, while the probability that it will be weak, P(A'), is 0.20 (i.e. these are prior probabilities). She wants to revise these probabilities by consulting an economic forecaster who does not have a perfect forecasting record. Let F1 be the event that he will forecast a strong economy. Based on his past record, we are told that P(F1|A) = 0.40 and P(F1|A') = 0.73. Using this information, compute the revised probabilities. That is, compute P(A|F1) Blank 1 and P(A'|F1) Blank 2. Give your answers to four decimal places.

a subway train in a certain line runs after every half hour, between every midnight and 6 in the morning. what is the probability that a man entering the station at random will have to wait at least 20 minutes?

A linear regression has b = 3 and a = 4. What is the predicted Y for X = 7?

If the five numbers {3, 4, 7, x, y} have a mean of 5 and a standard deviation of the square root of 2, find x and y given that y > x

In a factory turning out razor blade, there is a small chance of 1/500 for any blade to be defective. The blades are supplied in a packet of 10. Use Poisson distribution to calculate the approximate number of packets containing blades with no defective, one defective, two defectives and three defectives in a consignment of 10,000 packets

41 republicans, 2 Independent, 57 Democrats
If 3 senators are selected at random at random, what is the probability that they will all be republicans? What is the possibility they will all be Democrats? What is the probability that there will be 1 from each party, including the Independent?