Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Experience the convenience of getting accurate answers to your questions from a dedicated community of professionals. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
Answer:
They should guarantee the lifetime of their batteries for 32 months.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 36 months and a standard deviation of 2 months.
This means that [tex]\mu = 36, \sigma = 2[/tex]
If the company wants to replace no more than 2% of all batteries, for how many months should they guarantee the lifetime of their batteries?
The guarantee should be the 2th percentile of lengths, which is X when Z has a pvalue of 0.02. So X when Z = -2.054.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-2.054 = \frac{X - 36}{2}[/tex]
[tex]X - 36 = -2.054*2[/tex]
[tex]X = 31.89[/tex]
Rounding to the closest month, 32.
They should guarantee the lifetime of their batteries for 32 months.
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.
