Homework SourseStudies have shown that the random variable X the processing
Studies have shown that the random variable X, the processing time required to do a miltiplication on a new 3-D computer, is normally distributed with mean u and standard deviation 2 microseconds. A random sample of 16 observations is to be taken.
A. What is the distribution of X\'
B. These data are obtained
42.65 45.15 39.32 44.44 41.63 41.54 41.59 45.68 46.50 41.35 44.37 40.27 43.87 43.79 43.28 40.70
Based on these data, find an unbiased estimate for u.
C. Find a 95% confidence interval for u. Would you be surprised to read that the average time required to process a multiplication on this system is 42.2 microseconds? Explain using the confidence interval.
Solution
A. X\' follows normal distribution with mean u and standard deviation 2/sqrt(16)
B. unbiased estimate = sample mean = 42.8831
C.
| Sample Mean = 1220.44 SD = 32.8714 Sample Size (n) = 9 Standard Error (SE) = SD/root(n) = 10.9571 alpha (a) = 1-0.85 = 0.15 we use t-distribution as population standard deviation is unknown t(a/2, n-1 ) = 1.5922 Margin of Error (ME) = t(a/2,n-1)x SE = 17.4459 85% confidence interval is given by: Sample Mean +/- (Margin of Error) 1220.44 +/- 17.4459 = (1202.9941 , 1237.8859) |
