IDNLearn.com is your go-to resource for finding answers to any question you have. Our platform offers reliable and comprehensive answers to help you make informed decisions quickly and easily.
Sagot :
Using the normal distribution, it is found that there is a 0.2776 = 27.76% probability that the life span of the monitor will be more than 20,179 hours.
Normal Probability Distribution
The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The mean and the standard deviation are given, respectively, by:
[tex]\mu = 19000, \sigma = \sqrt{4000000} = 2000[/tex]
The probability that the life span of the monitor will be more than 20,179 hours is one subtracted by the p-value of Z when X = 20179, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20179 - 19000}{2000}[/tex]
Z = 0.59.
Z = 0.59 has a p-value of 0.7224.
1 - 0.7224 = 0.2776.
0.2776 = 27.76% probability that the life span of the monitor will be more than 20,179 hours.
More can be learned about the normal distribution at https://brainly.com/question/24663213
#SPJ1
Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. IDNLearn.com is your go-to source for accurate answers. Thanks for stopping by, and come back for more helpful information.
