3-52. Operators of a medical linear accelerator are inter- ested in estimating the number of hours until the first software failure. Prior experience has shown that the time until failure is normally distributed with mean 1000 hours and standard de- viation 60 hours. (a) Find the probability that the software will not fail before 1140 hours of operation. (b) Find the probability that the software will fail within 900 hours of operation.
3-52. Operators of a medical linear accelerator are inter- ested in estimating the number of hours until the first software failure. Prior experience has shown that the time until failure is normally distributed with mean 1000 hours and standard de- viation 60 hours. (a) Find the probability that the software will not fail before 1140 hours of operation. (b) Find the probability that the software will fail within 900 hours of operation.
3-52. Operators of a medical linear accelerator are inter- ested in estimating the number of hours until the first software failure. Prior experience has shown that the time until failure is normally distributed with mean 1000 hours and standard de- viation 60 hours. (a) Find the probability that the software will not fail before 1140 hours of operation. (b) Find the probability that the software will fail within 900 hours of operation.
Standardize to the standard Normal distribution. Draw a sketch of the original distribution
Transcribed Image Text:3-52. Operators of a medical linear accelerator are inter-
ested in estimating the number of hours until the first software
failure. Prior experience has shown that the time until failure
is normally distributed with mean 1000 hours and standard de-
viation 60 hours.
(a) Find the probability that the software will not fail before
1140 hours of operation.
(b) Find the probability that the software will fail within 900
hours of operation.
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
Expert Solution
Step 1
a)
Consider that the mean and standard deviation of a random variable X are µ and σ, respectively.
Thus, the z-score of that random variable X is z = (X – µ)/σ.
